Physics
General
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Question

A body of mass m rests on horizontal surface. The coefficient of friction between the body and the surface is if the body is pulled by a force P as shown in figure the limiting function between body and surface will be……..

  1. mg
  2. open square brackets m g plus P over 2 close square brackets
  3. open square brackets m g minus P over 2 close square brackets
  4. open square brackets M G minus fraction numerator square root of 3 P end root over denominator 2 end fraction close square brackets

The correct answer is: open square brackets m g minus P over 2 close square brackets

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Related Questions to study

General
physics

A block of mass 300 kg is set into motion on a frictionless horizontal surface with the help of frictionless pulley and a rope system as shown in figure. What horizontal force F should be applied to produce in the block an acceleration of 1 ms-1

A block of mass 300 kg is set into motion on a frictionless horizontal surface with the help of frictionless pulley and a rope system as shown in figure. What horizontal force F should be applied to produce in the block an acceleration of 1 ms-1

physicsGeneral
General
Maths-

If f left parenthesis x right parenthesis is a polynomial function such that f space left parenthesis x right parenthesis f space open parentheses 1 over x close parentheses equals f left parenthesis x right parenthesis plus f space open parentheses 1 over x close parentheses text  and  end text f space left parenthesis 3 right parenthesis equals negative 80 text  then  end text f left parenthesis x right parenthesis minus f space open parentheses 1 over x close parentheses equals

G i v e n comma space
space space space space space space space space space f open parentheses x close parentheses f open parentheses 1 over x close parentheses equals f open parentheses x close parentheses plus f open parentheses 1 over x close parentheses
rightwards double arrow f open parentheses x close parentheses f open parentheses 1 over x close parentheses minus f open parentheses 1 over x close parentheses equals f open parentheses x close parentheses
rightwards double arrow f open parentheses 1 over x close parentheses open square brackets f open parentheses x close parentheses minus 1 close square brackets equals f open parentheses x close parentheses space space _ _ _ _ _ _ _ _ _ _ left parenthesis i right parenthesis

G i v e n comma space
space space space space space space space space space space f open parentheses x close parentheses f open parentheses 1 over x close parentheses equals f open parentheses x close parentheses plus f open parentheses 1 over x close parentheses
rightwards double arrow f open parentheses x close parentheses f open parentheses 1 over x close parentheses minus f open parentheses x close parentheses space equals f open parentheses 1 over x close parentheses
rightwards double arrow f open parentheses x close parentheses open square brackets f open parentheses 1 over x close parentheses minus 1 close square brackets equals f open parentheses 1 over x close parentheses space _ _ _ _ _ _ _ _ _ _ left parenthesis i i right parenthesis

M u l t i p l y i n g space e q u a t i o n space left parenthesis i right parenthesis space a n d space left parenthesis i i right parenthesis comma space w e space g e t colon
f open parentheses 1 over x close parentheses open square brackets f open parentheses x close parentheses minus 1 close square brackets. space f open parentheses x close parentheses open square brackets f open parentheses 1 over x close parentheses minus 1 close square brackets equals f open parentheses x close parentheses f open parentheses 1 over x close parentheses
rightwards double arrow open square brackets f open parentheses x close parentheses minus 1 close square brackets. open square brackets f open parentheses 1 over x close parentheses minus 1 close square brackets equals 1 space space _ _ _ _ _ _ _ _ left parenthesis i i i right parenthesis

N o w comma space l e t space g left parenthesis x right parenthesis space equals space f open parentheses x close parentheses minus 1 space a n d space g open parentheses 1 over x close parentheses equals space f open parentheses 1 over x close parentheses minus 1
S o comma space e q u a t i o n space left parenthesis i i i right parenthesis space i s comma space
rightwards double arrow g left parenthesis x right parenthesis. g open parentheses 1 over x close parentheses equals 1
T h u s comma space g left parenthesis x right parenthesis equals plus-or-minus x to the power of n space end exponent space space a n d space space g open parentheses 1 over x close parentheses equals plus-or-minus 1 over x to the power of n
S o comma space f left parenthesis x right parenthesis equals plus-or-minus x to the power of n plus 1 space a n d space f open parentheses 1 over x close parentheses equals plus-or-minus 1 over x to the power of n plus 1

f left parenthesis 3 right parenthesis equals plus-or-minus 3 to the power of n plus 1
rightwards double arrow negative 80 equals plus-or-minus 3 to the power of n plus 1
rightwards double arrow negative 81 equals plus-or-minus 3 to the power of n
rightwards double arrow negative 81 equals negative 3 to the power of n
rightwards double arrow 3 to the power of 4 equals 3 to the power of n
rightwards double arrow n space equals space 4

S o comma space f left parenthesis x right parenthesis equals negative x to the power of 4 plus 1 space a n d space f open parentheses 1 over x close parentheses equals fraction numerator negative 1 over denominator x to the power of 4 end fraction plus 1

f left parenthesis x right parenthesis space plus space f open parentheses 1 over x close parentheses space
equals space minus x to the power of 4 plus 1 minus open square brackets fraction numerator negative 1 over denominator x to the power of 4 end fraction plus 1 close square brackets
equals negative x to the power of 4 plus 1 plus 1 over x to the power of 4 minus 1
equals 1 over x to the power of 4 minus x to the power of 4

If f left parenthesis x right parenthesis is a polynomial function such that f space left parenthesis x right parenthesis f space open parentheses 1 over x close parentheses equals f left parenthesis x right parenthesis plus f space open parentheses 1 over x close parentheses text  and  end text f space left parenthesis 3 right parenthesis equals negative 80 text  then  end text f left parenthesis x right parenthesis minus f space open parentheses 1 over x close parentheses equals

Maths-General
G i v e n comma space
space space space space space space space space space f open parentheses x close parentheses f open parentheses 1 over x close parentheses equals f open parentheses x close parentheses plus f open parentheses 1 over x close parentheses
rightwards double arrow f open parentheses x close parentheses f open parentheses 1 over x close parentheses minus f open parentheses 1 over x close parentheses equals f open parentheses x close parentheses
rightwards double arrow f open parentheses 1 over x close parentheses open square brackets f open parentheses x close parentheses minus 1 close square brackets equals f open parentheses x close parentheses space space _ _ _ _ _ _ _ _ _ _ left parenthesis i right parenthesis

G i v e n comma space
space space space space space space space space space space f open parentheses x close parentheses f open parentheses 1 over x close parentheses equals f open parentheses x close parentheses plus f open parentheses 1 over x close parentheses
rightwards double arrow f open parentheses x close parentheses f open parentheses 1 over x close parentheses minus f open parentheses x close parentheses space equals f open parentheses 1 over x close parentheses
rightwards double arrow f open parentheses x close parentheses open square brackets f open parentheses 1 over x close parentheses minus 1 close square brackets equals f open parentheses 1 over x close parentheses space _ _ _ _ _ _ _ _ _ _ left parenthesis i i right parenthesis

M u l t i p l y i n g space e q u a t i o n space left parenthesis i right parenthesis space a n d space left parenthesis i i right parenthesis comma space w e space g e t colon
f open parentheses 1 over x close parentheses open square brackets f open parentheses x close parentheses minus 1 close square brackets. space f open parentheses x close parentheses open square brackets f open parentheses 1 over x close parentheses minus 1 close square brackets equals f open parentheses x close parentheses f open parentheses 1 over x close parentheses
rightwards double arrow open square brackets f open parentheses x close parentheses minus 1 close square brackets. open square brackets f open parentheses 1 over x close parentheses minus 1 close square brackets equals 1 space space _ _ _ _ _ _ _ _ left parenthesis i i i right parenthesis

N o w comma space l e t space g left parenthesis x right parenthesis space equals space f open parentheses x close parentheses minus 1 space a n d space g open parentheses 1 over x close parentheses equals space f open parentheses 1 over x close parentheses minus 1
S o comma space e q u a t i o n space left parenthesis i i i right parenthesis space i s comma space
rightwards double arrow g left parenthesis x right parenthesis. g open parentheses 1 over x close parentheses equals 1
T h u s comma space g left parenthesis x right parenthesis equals plus-or-minus x to the power of n space end exponent space space a n d space space g open parentheses 1 over x close parentheses equals plus-or-minus 1 over x to the power of n
S o comma space f left parenthesis x right parenthesis equals plus-or-minus x to the power of n plus 1 space a n d space f open parentheses 1 over x close parentheses equals plus-or-minus 1 over x to the power of n plus 1

f left parenthesis 3 right parenthesis equals plus-or-minus 3 to the power of n plus 1
rightwards double arrow negative 80 equals plus-or-minus 3 to the power of n plus 1
rightwards double arrow negative 81 equals plus-or-minus 3 to the power of n
rightwards double arrow negative 81 equals negative 3 to the power of n
rightwards double arrow 3 to the power of 4 equals 3 to the power of n
rightwards double arrow n space equals space 4

S o comma space f left parenthesis x right parenthesis equals negative x to the power of 4 plus 1 space a n d space f open parentheses 1 over x close parentheses equals fraction numerator negative 1 over denominator x to the power of 4 end fraction plus 1

f left parenthesis x right parenthesis space plus space f open parentheses 1 over x close parentheses space
equals space minus x to the power of 4 plus 1 minus open square brackets fraction numerator negative 1 over denominator x to the power of 4 end fraction plus 1 close square brackets
equals negative x to the power of 4 plus 1 plus 1 over x to the power of 4 minus 1
equals 1 over x to the power of 4 minus x to the power of 4
General
physics

A body of mass. 5 kg starts motion form the origin with an initial velocity Error converting from MathML to accessible text. If a constant force Error converting from MathML to accessible text. acts an the body, than the time in which the Y-component of the velocity becomes zero is……

A body of mass. 5 kg starts motion form the origin with an initial velocity Error converting from MathML to accessible text. If a constant force Error converting from MathML to accessible text. acts an the body, than the time in which the Y-component of the velocity becomes zero is……

physicsGeneral
General
physics-

An L -shaped tube with a small office is held in a water stream as shown in fig. The upper end of the tube is? 10.6cm above the surface of water. What will be the. height of the set of water coming from the office velocity of water stream is 2.45 m/s2

   

An L -shaped tube with a small office is held in a water stream as shown in fig. The upper end of the tube is? 10.6cm above the surface of water. What will be the. height of the set of water coming from the office velocity of water stream is 2.45 m/s2

physics-General
   
General
Maths-

f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left left columnspacing 1em end attributes row cell left square bracket x right square bracket      text  if  end text minus 3 less than x less or equal than negative 1 end cell row cell vertical line x vertical line      text  if  end text minus 1 less than x less than 1 end cell row cell vertical line left square bracket negative x right square bracket vertical line      text  if  end text 1 less or equal than x less or equal than 3 end cell end table text  then  end text left curly bracket x colon f left parenthesis x right parenthesis greater or equal than 0 right curly bracket equals close

For, f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left left columnspacing 1em end attributes row cell left square bracket x right square bracket      text  if  end text minus 3 less than x less or equal than negative 1 end cell row cell vertical line x vertical line      text  if  end text minus 1 less than x less than 1 end cell row cell vertical line left square bracket negative x right square bracket vertical line      text  if  end text 1 less or equal than x less or equal than 3 end cell end table close, we have to find x when f(x) will be greater than or equals to 0.
As per the given function,
f(x) will be negative whennegative 3 less than x less or equal than negative 1
f(x) will be positive or 0 when negative 1 less than x less than 1  (as f(x)= open vertical bar x close vertical bar)
f(x) will be positive when 1 less or equal than x less or equal than 3    (as f(x)= open vertical bar open square brackets negative x close square brackets close vertical bar)
So, for f left parenthesis x right parenthesis greater or equal than 0 comma space x equalsleft parenthesis negative 1 comma 3 right square bracket

f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left left columnspacing 1em end attributes row cell left square bracket x right square bracket      text  if  end text minus 3 less than x less or equal than negative 1 end cell row cell vertical line x vertical line      text  if  end text minus 1 less than x less than 1 end cell row cell vertical line left square bracket negative x right square bracket vertical line      text  if  end text 1 less or equal than x less or equal than 3 end cell end table text  then  end text left curly bracket x colon f left parenthesis x right parenthesis greater or equal than 0 right curly bracket equals close

Maths-General
For, f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left left columnspacing 1em end attributes row cell left square bracket x right square bracket      text  if  end text minus 3 less than x less or equal than negative 1 end cell row cell vertical line x vertical line      text  if  end text minus 1 less than x less than 1 end cell row cell vertical line left square bracket negative x right square bracket vertical line      text  if  end text 1 less or equal than x less or equal than 3 end cell end table close, we have to find x when f(x) will be greater than or equals to 0.
As per the given function,
f(x) will be negative whennegative 3 less than x less or equal than negative 1
f(x) will be positive or 0 when negative 1 less than x less than 1  (as f(x)= open vertical bar x close vertical bar)
f(x) will be positive when 1 less or equal than x less or equal than 3    (as f(x)= open vertical bar open square brackets negative x close square brackets close vertical bar)
So, for f left parenthesis x right parenthesis greater or equal than 0 comma space x equalsleft parenthesis negative 1 comma 3 right square bracket
General
physics

Same forces act an two bodies of different mass 2 kg and 5 kg initially at rest. The ratio of times. required to acquire same final velocity is…..

Same forces act an two bodies of different mass 2 kg and 5 kg initially at rest. The ratio of times. required to acquire same final velocity is…..

physicsGeneral
General
physics

An object of mass 3 kg is moving with a velocity of 5 m/s along a stright path. If a force of 12 N is applied for 3 sec on the object in a perpendicular to its direction of motion. The magnitude of velocity of the particle at the end of 3 sec is……..m/s.

An object of mass 3 kg is moving with a velocity of 5 m/s along a stright path. If a force of 12 N is applied for 3 sec on the object in a perpendicular to its direction of motion. The magnitude of velocity of the particle at the end of 3 sec is……..m/s.

physicsGeneral
General
physics

A rope which can withstand a maximum tension of 400 N hangs from a tree. If a monkey of mass 30 kg climbs on the rope in which of the following cases-will the rope break? (take g=10 ms2 and neglect the mass of rope)

A rope which can withstand a maximum tension of 400 N hangs from a tree. If a monkey of mass 30 kg climbs on the rope in which of the following cases-will the rope break? (take g=10 ms2 and neglect the mass of rope)

physicsGeneral
General
Maths-

Let g left parenthesis x right parenthesis equals 1 plus x minus left square bracket x right square bracket text  and  end text f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left left columnspacing 1em end attributes row cell negative 1 comma      text  if  end text x less than 0 end cell row cell 0      text  if  end text x equals 0 text  then  end text fraction numerator f left parenthesis g left parenthesis 2009 right parenthesis right parenthesis over denominator g left parenthesis f left parenthesis 2009 right parenthesis right parenthesis end fraction equals end cell row cell 1 comma      text  if  end text x greater than 0 end cell end table close

For g left parenthesis x right parenthesis equals 1 plus x minus left square bracket x right square bracket text   and   end text f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left left columnspacing 1em end attributes row cell negative 1 comma      text  if  end text x less than 0 end cell row cell 0      text  if  end text x equals 0 end cell row cell 1 comma      text  if  end text x greater than 0 end cell end table close
f(g(x))=f(1+x-open square brackets x close square brackets)
f(g(2009))= f (1+2009-open square brackets 2009 close square brackets)
= f (1+2009-2009)
= f (1)
=1  (as x is greater than 0)
g(f(x))=g(f(2009))
= g(1)     (f(2009)=0 as x is greater than 0)
=1+1-open square brackets 1 close square brackets
=2+1
=1
S o comma space fraction numerator f left parenthesis g left parenthesis 2009 right parenthesis right parenthesis over denominator g left parenthesis f left parenthesis 2009 right parenthesis right parenthesis end fraction equals 1 over 1 equals 1

Let g left parenthesis x right parenthesis equals 1 plus x minus left square bracket x right square bracket text  and  end text f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left left columnspacing 1em end attributes row cell negative 1 comma      text  if  end text x less than 0 end cell row cell 0      text  if  end text x equals 0 text  then  end text fraction numerator f left parenthesis g left parenthesis 2009 right parenthesis right parenthesis over denominator g left parenthesis f left parenthesis 2009 right parenthesis right parenthesis end fraction equals end cell row cell 1 comma      text  if  end text x greater than 0 end cell end table close

Maths-General
For g left parenthesis x right parenthesis equals 1 plus x minus left square bracket x right square bracket text   and   end text f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left left columnspacing 1em end attributes row cell negative 1 comma      text  if  end text x less than 0 end cell row cell 0      text  if  end text x equals 0 end cell row cell 1 comma      text  if  end text x greater than 0 end cell end table close
f(g(x))=f(1+x-open square brackets x close square brackets)
f(g(2009))= f (1+2009-open square brackets 2009 close square brackets)
= f (1+2009-2009)
= f (1)
=1  (as x is greater than 0)
g(f(x))=g(f(2009))
= g(1)     (f(2009)=0 as x is greater than 0)
=1+1-open square brackets 1 close square brackets
=2+1
=1
S o comma space fraction numerator f left parenthesis g left parenthesis 2009 right parenthesis right parenthesis over denominator g left parenthesis f left parenthesis 2009 right parenthesis right parenthesis end fraction equals 1 over 1 equals 1
General
physics-

A thin liquid film formed between a u-shaped wire and a light slider supports a weight of 1.5 cross times 10 to the power of negative 2 end exponent text end text N (see figure). The length of the slider is 30 cm and its weight negligible. The surface tension of the liquid film is.

A thin liquid film formed between a u-shaped wire and a light slider supports a weight of 1.5 cross times 10 to the power of negative 2 end exponent text end text N (see figure). The length of the slider is 30 cm and its weight negligible. The surface tension of the liquid film is.

physics-General
General
physics

Three  masses 1 kg and 6 kg and 3 kg are connected to each other with threads and are placed on a table as shown in figure. The acceleration with which the system is moving is-ms2(g=10ms2)

Three  masses 1 kg and 6 kg and 3 kg are connected to each other with threads and are placed on a table as shown in figure. The acceleration with which the system is moving is-ms2(g=10ms2)

physicsGeneral
General
physics-

The point of maximum and minimum attraction in the curve between potential energy (U) and distance (r) of a diatomic molecules are respectively.

The point of maximum and minimum attraction in the curve between potential energy (U) and distance (r) of a diatomic molecules are respectively.

physics-General
General
physics-

Which are of the following is the young's modulus (in open N divided by m squared close parentheses for the wire having the stress strain curve in the figure.

Which are of the following is the young's modulus (in open N divided by m squared close parentheses for the wire having the stress strain curve in the figure.

physics-General
General
physics

If the surfaces shown in figure are frictionless, the ratio of T1 and T2 is……..

If the surfaces shown in figure are frictionless, the ratio of T1 and T2 is……..

physicsGeneral
General
physics

Three  blocks of masers m1,m2 and  by massless strings as shown in figure, on a frictionless table. They are Pulled with the force T3=40 N. If  m1=10 kg,m2=6 kg and m3=4kg the tension T2  will  be=...N

Three  blocks of masers m1,m2 and  by massless strings as shown in figure, on a frictionless table. They are Pulled with the force T3=40 N. If  m1=10 kg,m2=6 kg and m3=4kg the tension T2  will  be=...N

physicsGeneral