Physics-
General
Easy

Question

An object is dropped from rest. Its v-t graph is

The correct answer is:


    Using
    V equals u plus a t
    V equals g t(i)
    Comparing with y equals m x plus c
    Equation (i) represents a straight line passing through origin inclined x-axis (slope -g)

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    Related Questions to study

    General
    physics-

    In circuit shown below, the resistances are given in ohm and the battery is assumed ideal with emf equal to 3V. The voltage across the resistance R subscript 4 end subscript is

    Equivalent resistance of the given network
    R subscript e q end subscript equals 75 capital omega
    ∴ Total current through battery,
    i equals fraction numerator 3 over denominator 75 end fraction
    i subscript 1 end subscript equals i subscript 2 end subscript equals fraction numerator 3 over denominator 75 cross times 2 end fraction equals fraction numerator 3 over denominator 150 end fraction

    Current through resistance
    R subscript 4 end subscript equals fraction numerator 3 over denominator 150 end fraction cross times fraction numerator 60 over denominator open parentheses 30 plus 60 close parentheses end fraction
    equals fraction numerator 3 over denominator 150 end fraction cross times fraction numerator 60 over denominator 90 end fraction
    equals fraction numerator 2 over denominator 150 end fraction A
    V subscript 4 end subscript equals i subscript 4 end subscript cross times R subscript 4 end subscript
    equals fraction numerator 2 over denominator 150 end fraction cross times 30
    equals fraction numerator 2 over denominator 5 end fraction equals 0.4 blank v o l t

    In circuit shown below, the resistances are given in ohm and the battery is assumed ideal with emf equal to 3V. The voltage across the resistance R subscript 4 end subscript is

    physics-General
    Equivalent resistance of the given network
    R subscript e q end subscript equals 75 capital omega
    ∴ Total current through battery,
    i equals fraction numerator 3 over denominator 75 end fraction
    i subscript 1 end subscript equals i subscript 2 end subscript equals fraction numerator 3 over denominator 75 cross times 2 end fraction equals fraction numerator 3 over denominator 150 end fraction

    Current through resistance
    R subscript 4 end subscript equals fraction numerator 3 over denominator 150 end fraction cross times fraction numerator 60 over denominator open parentheses 30 plus 60 close parentheses end fraction
    equals fraction numerator 3 over denominator 150 end fraction cross times fraction numerator 60 over denominator 90 end fraction
    equals fraction numerator 2 over denominator 150 end fraction A
    V subscript 4 end subscript equals i subscript 4 end subscript cross times R subscript 4 end subscript
    equals fraction numerator 2 over denominator 150 end fraction cross times 30
    equals fraction numerator 2 over denominator 5 end fraction equals 0.4 blank v o l t
    General
    physics-

    The resistance across A blank a n d blank Bin the figure below will be

    Resistance are in parallel
    therefore blank R subscript e q end subscript equals fraction numerator R over denominator 3 end fraction

    The resistance across A blank a n d blank Bin the figure below will be

    physics-General
    Resistance are in parallel
    therefore blank R subscript e q end subscript equals fraction numerator R over denominator 3 end fraction
    General
    physics-

    Five equal resistances, each of resistance R commaare connected as shown in figure below. A bettery of V volt is connected between A blank a n d blank B.The current flowing in F C will be

    I equals fraction numerator V over denominator R end fraction

    therefore blank C u r r e n t blank i n blank F C equals fraction numerator 1 over denominator 2 end fraction equals fraction numerator V over denominator 2 R end fraction

    Five equal resistances, each of resistance R commaare connected as shown in figure below. A bettery of V volt is connected between A blank a n d blank B.The current flowing in F C will be

    physics-General
    I equals fraction numerator V over denominator R end fraction

    therefore blank C u r r e n t blank i n blank F C equals fraction numerator 1 over denominator 2 end fraction equals fraction numerator V over denominator 2 R end fraction
    General
    Maths-

    If f left parenthesis x right parenthesis equals sin squared space open parentheses pi over 8 plus x over 2 close parentheses minus sin squared space open parentheses pi over 8 minus x over 2 close parentheses, then the period of f(x) is

    f left parenthesis x right parenthesis equals sin squared space open parentheses pi over 8 plus x over 2 close parentheses minus sin squared space open parentheses straight pi over 8 minus x over 2 close parentheses
equals 1 half open square brackets 1 minus cos 2 open parentheses straight pi over 8 plus x over 2 close parentheses space close square brackets minus 1 half open square brackets 1 minus cos 2 open parentheses straight pi over 8 minus x over 2 close parentheses close square brackets
equals 1 half open square brackets 1 minus cos open parentheses straight pi over 4 plus x close parentheses space close square brackets minus 1 half open square brackets 1 minus cos open parentheses straight pi over 4 minus x close parentheses close square brackets
equals 1 half open square brackets cos open parentheses straight pi over 4 minus x close parentheses minus cos open parentheses straight pi over 4 plus x close parentheses close square brackets
equals 1 half open square brackets cos straight pi over 4. cos x space plus sin straight pi over 4 sin x space minus cos straight pi over 4 cos x plus sin straight pi over 4 sin x close square brackets
equals 1 half open square brackets 2 sin straight pi over 4 sin x close square brackets
equals fraction numerator 1 over denominator square root of 2 end fraction sin x space
f u n d a m e n t a l space p e r i o d space o f space sin a x space i s space fraction numerator 2 straight pi over denominator a end fraction.
S o comma space p e r i o d space o f space fraction numerator 1 over denominator square root of 2 end fraction sin x equals 2 straight pi

    If f left parenthesis x right parenthesis equals sin squared space open parentheses pi over 8 plus x over 2 close parentheses minus sin squared space open parentheses pi over 8 minus x over 2 close parentheses, then the period of f(x) is

    Maths-General
    f left parenthesis x right parenthesis equals sin squared space open parentheses pi over 8 plus x over 2 close parentheses minus sin squared space open parentheses straight pi over 8 minus x over 2 close parentheses
equals 1 half open square brackets 1 minus cos 2 open parentheses straight pi over 8 plus x over 2 close parentheses space close square brackets minus 1 half open square brackets 1 minus cos 2 open parentheses straight pi over 8 minus x over 2 close parentheses close square brackets
equals 1 half open square brackets 1 minus cos open parentheses straight pi over 4 plus x close parentheses space close square brackets minus 1 half open square brackets 1 minus cos open parentheses straight pi over 4 minus x close parentheses close square brackets
equals 1 half open square brackets cos open parentheses straight pi over 4 minus x close parentheses minus cos open parentheses straight pi over 4 plus x close parentheses close square brackets
equals 1 half open square brackets cos straight pi over 4. cos x space plus sin straight pi over 4 sin x space minus cos straight pi over 4 cos x plus sin straight pi over 4 sin x close square brackets
equals 1 half open square brackets 2 sin straight pi over 4 sin x close square brackets
equals fraction numerator 1 over denominator square root of 2 end fraction sin x space
f u n d a m e n t a l space p e r i o d space o f space sin a x space i s space fraction numerator 2 straight pi over denominator a end fraction.
S o comma space p e r i o d space o f space fraction numerator 1 over denominator square root of 2 end fraction sin x equals 2 straight pi
    General
    physics-

    The plot represents the flow of current through a wire at three different times.

    The ratio of charges flowing through the wire at different times is

    ) 2 : 3 : 3
    Therefore, charge is equal to area under the curve.
    ∴ Ist rectangle =q=lb=2
    IInd rectangle =q=lb=2
    I I I r d blank t r i a n g l e equals q equals fraction numerator 1 over denominator 2 end fraction l b equals 2
    Hence, ratio is 1:1:1.

    The plot represents the flow of current through a wire at three different times.

    The ratio of charges flowing through the wire at different times is

    physics-General
    ) 2 : 3 : 3
    Therefore, charge is equal to area under the curve.
    ∴ Ist rectangle =q=lb=2
    IInd rectangle =q=lb=2
    I I I r d blank t r i a n g l e equals q equals fraction numerator 1 over denominator 2 end fraction l b equals 2
    Hence, ratio is 1:1:1.
    General
    physics-

    Consider a thin square sheet of side L and thickness t comma made of a material of resistivity rho. The resistance between two opposite faces, shown by the shaded areas in the figure is

    R equals fraction numerator rho open parentheses L close parentheses over denominator A end fraction equals fraction numerator rho L over denominator t L end fraction equals fraction numerator rho over denominator t end fraction
    i e comma blank R is independent of L.
    Hence the correct option is (c).

    Consider a thin square sheet of side L and thickness t comma made of a material of resistivity rho. The resistance between two opposite faces, shown by the shaded areas in the figure is

    physics-General
    R equals fraction numerator rho open parentheses L close parentheses over denominator A end fraction equals fraction numerator rho L over denominator t L end fraction equals fraction numerator rho over denominator t end fraction
    i e comma blank R is independent of L.
    Hence the correct option is (c).
    General
    physics-

    The time taken by a block of wood (initially at rest)to slide down a smooth inclined plane 9.8 blank mlong (angle of inclination is 30 degree) is

    For one dimensional motion along a plane
    S equals u t plus fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent rightwards double arrow 9.8 equals 0 plus fraction numerator 1 over denominator 2 end fraction g sin invisible function application blank 30 degree t to the power of 2 end exponent rightwards double arrow t equals 2 s e c

    The time taken by a block of wood (initially at rest)to slide down a smooth inclined plane 9.8 blank mlong (angle of inclination is 30 degree) is

    physics-General
    For one dimensional motion along a plane
    S equals u t plus fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent rightwards double arrow 9.8 equals 0 plus fraction numerator 1 over denominator 2 end fraction g sin invisible function application blank 30 degree t to the power of 2 end exponent rightwards double arrow t equals 2 s e c
    General
    physics-

    v minus t graph for a particle is as shown. The distance travelled in the first 4 blank s is

    Distance covered equalsArea enclosed by v minus t graph
    equals Area of triangle equals fraction numerator 1 over denominator 2 end fraction cross times 4 cross times 8 equals 16 blank m

    v minus t graph for a particle is as shown. The distance travelled in the first 4 blank s is

    physics-General
    Distance covered equalsArea enclosed by v minus t graph
    equals Area of triangle equals fraction numerator 1 over denominator 2 end fraction cross times 4 cross times 8 equals 16 blank m
    General
    Maths-

    Period of sin space x sin space open parentheses 120 to the power of ring operator minus x close parentheses sin space open parentheses 120 to the power of ring operator plus x close parentheses is

    sin space x sin space open parentheses 120 to the power of ring operator minus x close parentheses sin space open parentheses 120 to the power of ring operator plus x close parentheses
equals sin x space left parenthesis sin squared 120 degree minus sin squared x right parenthesis
equals sin x space open square brackets open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses squared minus sin squared x close square brackets
equals sin x space open square brackets 3 over 4 minus sin squared x close square brackets
equals 1 fourth open square brackets 3 space sin x space minus 4 sin squared x close square brackets
equals 1 fourth sin 3 x
f u n d a m e n t a l space p e r i o d space o f space sin space a x space i s space fraction numerator 2 straight pi over denominator a end fraction.
S o comma space p e r i o d space o f space 1 fourth sin 3 x space i s fraction numerator 2 straight pi over denominator 3 end fraction.

    Period of sin space x sin space open parentheses 120 to the power of ring operator minus x close parentheses sin space open parentheses 120 to the power of ring operator plus x close parentheses is

    Maths-General
    sin space x sin space open parentheses 120 to the power of ring operator minus x close parentheses sin space open parentheses 120 to the power of ring operator plus x close parentheses
equals sin x space left parenthesis sin squared 120 degree minus sin squared x right parenthesis
equals sin x space open square brackets open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses squared minus sin squared x close square brackets
equals sin x space open square brackets 3 over 4 minus sin squared x close square brackets
equals 1 fourth open square brackets 3 space sin x space minus 4 sin squared x close square brackets
equals 1 fourth sin 3 x
f u n d a m e n t a l space p e r i o d space o f space sin space a x space i s space fraction numerator 2 straight pi over denominator a end fraction.
S o comma space p e r i o d space o f space 1 fourth sin 3 x space i s fraction numerator 2 straight pi over denominator 3 end fraction.
    General
    physics-

    A particle starts from rest at t equals 0 and undergoes an acceleration a in m s to the power of negative 2 end exponent with time t in seconds which is as shown

    Which one of the following plot represents velocity V in m s to the power of negative 1 end exponent versus time t in seconds


    Takingthe motion from 0 to 2 blank s
    u equals 0 comma blank a equals 3 m s to the power of negative 2 end exponent comma blank t equals 2 s comma blank v equals ?
    v equals u plus a t equals 0 plus 3 cross times 2 equals 6 m s to the power of negative 1 end exponent
    Taking the motion from 2 blank s to 4 blank s
    v equals 6 plus open parentheses negative 3 close parentheses open parentheses 2 close parentheses equals 0 m s to the power of negative 1 end exponent

    A particle starts from rest at t equals 0 and undergoes an acceleration a in m s to the power of negative 2 end exponent with time t in seconds which is as shown

    Which one of the following plot represents velocity V in m s to the power of negative 1 end exponent versus time t in seconds

    physics-General

    Takingthe motion from 0 to 2 blank s
    u equals 0 comma blank a equals 3 m s to the power of negative 2 end exponent comma blank t equals 2 s comma blank v equals ?
    v equals u plus a t equals 0 plus 3 cross times 2 equals 6 m s to the power of negative 1 end exponent
    Taking the motion from 2 blank s to 4 blank s
    v equals 6 plus open parentheses negative 3 close parentheses open parentheses 2 close parentheses equals 0 m s to the power of negative 1 end exponent
    General
    Maths-

    Period of cos to the power of 6 space x plus sin to the power of 6 space x is

    By fundamental property of f(x) periodic function with period T.
    f (x+T) =f(x)
    let f (x) =cos to the power of 6 space x plus sin to the power of 6 space x
    assuming from the options smallest period of f(x) to be pi over 2.
    rightwards double arrow f left parenthesis x plus straight pi over 2 right parenthesis equals f left parenthesis x right parenthesis
rightwards double arrow cos to the power of 6 open parentheses x plus straight pi over 2 close parentheses plus sin to the power of 6 open parentheses x plus straight pi over 2 close parentheses equals cos to the power of 6 x plus sin to the power of 6 x
t h e r e f o r e space straight pi over 2 space i s space t h e space f u n d a m e n t a l space p e r i o d space o f space f left parenthesis x right parenthesis.

    Period of cos to the power of 6 space x plus sin to the power of 6 space x is

    Maths-General
    By fundamental property of f(x) periodic function with period T.
    f (x+T) =f(x)
    let f (x) =cos to the power of 6 space x plus sin to the power of 6 space x
    assuming from the options smallest period of f(x) to be pi over 2.
    rightwards double arrow f left parenthesis x plus straight pi over 2 right parenthesis equals f left parenthesis x right parenthesis
rightwards double arrow cos to the power of 6 open parentheses x plus straight pi over 2 close parentheses plus sin to the power of 6 open parentheses x plus straight pi over 2 close parentheses equals cos to the power of 6 x plus sin to the power of 6 x
t h e r e f o r e space straight pi over 2 space i s space t h e space f u n d a m e n t a l space p e r i o d space o f space f left parenthesis x right parenthesis.
    General
    physics-

    Two inclined planes are located as shown in figure. A particle is projected from the foot of one frictionless plane along its line with a velocity just sufficient to carry it to top after which the particle slides down the other frictionless inclined plane. The total time it will take to reach the point C is

    The time of ascent = time of descent equals t subscript 0 end subscript
    T equals total time of flight equals 2 t subscript 0 end subscript

    sin invisible function application 45 degree equals fraction numerator 9.8 over denominator B C end fraction equals fraction numerator 9.8 over denominator s end fraction
    therefore blank s equals 9.8 square root of 2
    therefore blank s equals u t plus fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent
    s equals 0 cross times t plus fraction numerator 1 over denominator 2 end fraction left parenthesis g sin invisible function application 45 degree right parenthesis t subscript 0 end subscript superscript 2 end superscript
    or 9.8 square root of 2 equals fraction numerator 9.8 over denominator 2 square root of 2 end fraction t subscript 0 end subscript superscript 2 end superscript
    therefore blank t subscript 0 end subscript superscript 2 end superscript equals 4
    therefore blank t subscript 0 end subscript equals 2 s
    therefore blank T equals 2 t subscript 0 end subscript minus 4 s

    Two inclined planes are located as shown in figure. A particle is projected from the foot of one frictionless plane along its line with a velocity just sufficient to carry it to top after which the particle slides down the other frictionless inclined plane. The total time it will take to reach the point C is

    physics-General
    The time of ascent = time of descent equals t subscript 0 end subscript
    T equals total time of flight equals 2 t subscript 0 end subscript

    sin invisible function application 45 degree equals fraction numerator 9.8 over denominator B C end fraction equals fraction numerator 9.8 over denominator s end fraction
    therefore blank s equals 9.8 square root of 2
    therefore blank s equals u t plus fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent
    s equals 0 cross times t plus fraction numerator 1 over denominator 2 end fraction left parenthesis g sin invisible function application 45 degree right parenthesis t subscript 0 end subscript superscript 2 end superscript
    or 9.8 square root of 2 equals fraction numerator 9.8 over denominator 2 square root of 2 end fraction t subscript 0 end subscript superscript 2 end superscript
    therefore blank t subscript 0 end subscript superscript 2 end superscript equals 4
    therefore blank t subscript 0 end subscript equals 2 s
    therefore blank T equals 2 t subscript 0 end subscript minus 4 s
    General
    physics-

    I minus Vcharacteristic of a copper wire of length L and area of cross-section A is shown in figure. The slope of the curve becomes

    Slope of graph
    equals fraction numerator I over denominator V end fraction equals fraction numerator 1 over denominator R end fraction
    If experiment is performed at higher temperature then resistance increase and hence slope decrease, choice (a) is wrong.
    Similarly in choice (b) and (c) resistance increase.
    But for choice (d) resistance R increases, so slope decreases

    I minus Vcharacteristic of a copper wire of length L and area of cross-section A is shown in figure. The slope of the curve becomes

    physics-General
    Slope of graph
    equals fraction numerator I over denominator V end fraction equals fraction numerator 1 over denominator R end fraction
    If experiment is performed at higher temperature then resistance increase and hence slope decrease, choice (a) is wrong.
    Similarly in choice (b) and (c) resistance increase.
    But for choice (d) resistance R increases, so slope decreases
    General
    physics-

    Four concurrent coplanar forces in newton are acting at a point and keep it in equilibrium figure. Then values of F and theta are

    In equilibrium position along y-direction
    2 sin 60degree equals square root of 3 plus F cos invisible function application theta
    or 2 cross times fraction numerator square root of 3 over denominator 2 end fraction equals square root of 3 plus F cos invisible function application theta or F cos invisible function application theta equals 0
    As F not equal to 0
    therefore blank cos invisible function application theta equals 0 or theta equals 90 degree
    Along x-direction, F blank s i n 90 degree equals 1 plus 2 c o s 60 degree
    equals 1 plus 2 cross times fraction numerator 1 over denominator 2 end fraction
    F equals 2N

    Four concurrent coplanar forces in newton are acting at a point and keep it in equilibrium figure. Then values of F and theta are

    physics-General
    In equilibrium position along y-direction
    2 sin 60degree equals square root of 3 plus F cos invisible function application theta
    or 2 cross times fraction numerator square root of 3 over denominator 2 end fraction equals square root of 3 plus F cos invisible function application theta or F cos invisible function application theta equals 0
    As F not equal to 0
    therefore blank cos invisible function application theta equals 0 or theta equals 90 degree
    Along x-direction, F blank s i n 90 degree equals 1 plus 2 c o s 60 degree
    equals 1 plus 2 cross times fraction numerator 1 over denominator 2 end fraction
    F equals 2N
    General
    physics-

    The effective capacitance between points X and Y shown in figure. Assuming C subscript 2 end subscript equals 10 blank muF and that outer capacitors are all 4 blank muF is

    The arrangement shows a Wheatstone bridge.
    As fraction numerator C subscript 1 end subscript over denominator C subscript 3 end subscript end fraction equals fraction numerator C subscript 4 end subscript over denominator C subscript 5 end subscript end fraction equals 1 comma blanktherefore the bridge is balanced.
    fraction numerator 1 over denominator C subscript s subscript 1 end subscript end subscript end fraction equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 4 end fraction equals fraction numerator 2 over denominator 4 end fraction equals fraction numerator 1 over denominator 2 end fraction comma C subscript s subscript 1 end subscript end subscript equals 2 mu blank F
    Similarly, C subscript s end subscript subscript 2 end subscript equals 2 mu blank F
    therefore effective capacitance
    equals C subscript p end subscript equals C subscript s end subscript subscript 1 end subscript plus C subscript s end subscript subscript 2 end subscript equals 2 plus 2 plus equals 4 mu blank F

    The effective capacitance between points X and Y shown in figure. Assuming C subscript 2 end subscript equals 10 blank muF and that outer capacitors are all 4 blank muF is

    physics-General
    The arrangement shows a Wheatstone bridge.
    As fraction numerator C subscript 1 end subscript over denominator C subscript 3 end subscript end fraction equals fraction numerator C subscript 4 end subscript over denominator C subscript 5 end subscript end fraction equals 1 comma blanktherefore the bridge is balanced.
    fraction numerator 1 over denominator C subscript s subscript 1 end subscript end subscript end fraction equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 4 end fraction equals fraction numerator 2 over denominator 4 end fraction equals fraction numerator 1 over denominator 2 end fraction comma C subscript s subscript 1 end subscript end subscript equals 2 mu blank F
    Similarly, C subscript s end subscript subscript 2 end subscript equals 2 mu blank F
    therefore effective capacitance
    equals C subscript p end subscript equals C subscript s end subscript subscript 1 end subscript plus C subscript s end subscript subscript 2 end subscript equals 2 plus 2 plus equals 4 mu blank F