General
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A pendulum of mass m hangs from a support fixed to a trolley. The direction of the string when the trolley rolls up a plane of inclination  with acceleration a0 is

Physics-General

  1. theta equals tan to the power of negative 1 end exponent alpha
  2. theta equals tan to the power of negative 1 end exponent open parentheses straight a subscript 0 over straight g close parentheses
  3. theta equals tan to the power of negative 1 end exponent open parentheses straight g over straight a subscript 0 close parentheses
  4. theta equals tan to the power of negative 1 end exponent open parentheses fraction numerator a subscript 0 plus g sin alpha over denominator g cos alpha end fraction close parentheses

    Answer:The correct answer is: theta equals tan to the power of negative 1 end exponent open parentheses fraction numerator a subscript 0 plus g sin alpha over denominator g cos alpha end fraction close parentheses

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    In the situation shown in figure all the string are light and inextensible and pullies are light. There is no friction at any surface and all block are of cuboidal shape. A horizontal force of magnitude F is applied to right most free end of string in both cases of figure 1 and figure 2 as shown. At the instant shown, the tension in all strings are non zero. Let the magnitude of acceleration of large blocks (of mass M) in figure 1 and figure 2 area subscript 1 and  a subscript 2   respectively. Then:


    In the situation shown in figure all the string are light and inextensible and pullies are light. There is no friction at any surface and all block are of cuboidal shape. A horizontal force of magnitude F is applied to right most free end of string in both cases of figure 1 and figure 2 as shown. At the instant shown, the tension in all strings are non zero. Let the magnitude of acceleration of large blocks (of mass M) in figure 1 and figure 2 area subscript 1 and  a subscript 2   respectively. Then:


    physics-General
    General
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    A plank is held at an angle  to the horizontal (Fig.) on two fixed supports A and B. The plank can slide against the supports (without friction) because of its weight Mg. Acceleration and direction in which a man of mass m should move so that the plank does not move.

    A plank is held at an angle  to the horizontal (Fig.) on two fixed supports A and B. The plank can slide against the supports (without friction) because of its weight Mg. Acceleration and direction in which a man of mass m should move so that the plank does not move.

    physics-General
    General
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    A light spring balance hangs from the hook of the other light spring balance and a block of mass M kg hangs from the former one. Then the true statement about the scale reading is-

    A light spring balance hangs from the hook of the other light spring balance and a block of mass M kg hangs from the former one. Then the true statement about the scale reading is-

    physics-General
    General
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    A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of 5 space m s to the power of negative 2 end exponent , the reading of the spring balance will be-

    A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of 5 space m s to the power of negative 2 end exponent , the reading of the spring balance will be-

    physics-General
    General
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    A block of mass m1 lies on top of fixed wedge as shown in figure-1 and another block of mass m2 lies on top of wedge which is free to move as shown in figure-2. At time t = 0, both the blocks are released from rest from a vertical height h above the respective horizontal surface on which the wedge is placed as shown. There is no frcition between block and wedge in both the figures. Let T1 and T2 be the time taken by block in figure-1 and block in figure-2 respectively to just reach the horizontal surface, then :


    A block of mass m1 lies on top of fixed wedge as shown in figure-1 and another block of mass m2 lies on top of wedge which is free to move as shown in figure-2. At time t = 0, both the blocks are released from rest from a vertical height h above the respective horizontal surface on which the wedge is placed as shown. There is no frcition between block and wedge in both the figures. Let T1 and T2 be the time taken by block in figure-1 and block in figure-2 respectively to just reach the horizontal surface, then :


    physics-General
    General
    physics-

    System is shown in the figure. Assume that cylinder remains in contact with the two wedges. The velocity of cylinder is –

    System is shown in the figure. Assume that cylinder remains in contact with the two wedges. The velocity of cylinder is –

    physics-General
    General
    maths-

    Let f left parenthesis x right parenthesis equals x c o s to the power of negative 1 end exponent invisible function application left parenthesis negative s i n invisible function application vertical line x vertical line right parenthesis comma x element of open square brackets negative fraction numerator pi over denominator 2 end fraction comma fraction numerator pi over denominator 2 end fraction close square brackets, then which of the following is true?

    Let f left parenthesis x right parenthesis equals x c o s to the power of negative 1 end exponent invisible function application left parenthesis negative s i n invisible function application vertical line x vertical line right parenthesis comma x element of open square brackets negative fraction numerator pi over denominator 2 end fraction comma fraction numerator pi over denominator 2 end fraction close square brackets, then which of the following is true?

    maths-General
    General
    maths-

    For all twice differentiable functios f colon R rightwards arrow R, with f left parenthesis 0 right parenthesis equals f left parenthesis 1 right parenthesis equals f to the power of ´ end exponent left parenthesis 0 right parenthesis equals 0

    For all twice differentiable functios f colon R rightwards arrow R, with f left parenthesis 0 right parenthesis equals f left parenthesis 1 right parenthesis equals f to the power of ´ end exponent left parenthesis 0 right parenthesis equals 0

    maths-General
    General
    physics-

    The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle theta should be :–

    The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle theta should be :–

    physics-General
    General
    physics-

    A potential divider is used to give outputs of 2V and 3V from a 5V source, as shown in figure. Which combination of resistances, R1 , R2 and R3 gives the correct voltages?

    For resistors in series connection, current (I) is the same through the resistors. In other words, ratio of the voltage drop across each resistor with its resistance is the same.
    That is I equals fraction numerator 5 minus 3 over denominator R subscript 1 end subscript end fraction equals fraction numerator 3 minus 2 over denominator R subscript 2 end subscript end fraction equals fraction numerator 2 over denominator R subscript 3 end subscript end fraction text  i.e.,  end text R subscript 1 end subscript colon R subscript 2 end subscript colon R subscript 3 end subscript equals 2 colon 1 colon 2

    A potential divider is used to give outputs of 2V and 3V from a 5V source, as shown in figure. Which combination of resistances, R1 , R2 and R3 gives the correct voltages?

    physics-General
    For resistors in series connection, current (I) is the same through the resistors. In other words, ratio of the voltage drop across each resistor with its resistance is the same.
    That is I equals fraction numerator 5 minus 3 over denominator R subscript 1 end subscript end fraction equals fraction numerator 3 minus 2 over denominator R subscript 2 end subscript end fraction equals fraction numerator 2 over denominator R subscript 3 end subscript end fraction text  i.e.,  end text R subscript 1 end subscript colon R subscript 2 end subscript colon R subscript 3 end subscript equals 2 colon 1 colon 2
    General
    physics-

    A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by :–

    A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by :–

    physics-General
    General
    maths-

    6 to the power of 2 n end exponent minus 35 n minus 1 is divisible by_____ in N

    6 to the power of 2 n end exponent minus 35 n minus 1 is divisible by_____ in N

    maths-General
    General
    maths-

    Let f be a twice differentiable function on left parenthesis 1 , 6 right parenthesis. If f left parenthesis 2 right parenthesis equals 8, f to the power of ´ end exponent left parenthesis 2 right parenthesis equals 5 comma f to the power of ´ end exponent left parenthesis x right parenthesis greater or equal than 1 and f to the power of ´ left parenthesis x right parenthesis greater or equal than 4, for all x element of left parenthesis 1 , 6 right parenthesis, then colon

    Let f be a twice differentiable function on left parenthesis 1 , 6 right parenthesis. If f left parenthesis 2 right parenthesis equals 8, f to the power of ´ end exponent left parenthesis 2 right parenthesis equals 5 comma f to the power of ´ end exponent left parenthesis x right parenthesis greater or equal than 1 and f to the power of ´ left parenthesis x right parenthesis greater or equal than 4, for all x element of left parenthesis 1 , 6 right parenthesis, then colon

    maths-General
    General
    physics-

    A insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the surface and the insect is 1 third  . If the line joining the centre of the hemispherical surface to the insect makes an angle a with the vertical, the maximum possible value of  alpha is given :

    A insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the surface and the insect is 1 third  . If the line joining the centre of the hemispherical surface to the insect makes an angle a with the vertical, the maximum possible value of  alpha is given :

    physics-General
    General
    physics-

    In the circuit shown the capacitor of capacitance C is initially uncharged. Now the capacitor is connected in the circuit as shown. The charge passed through an imaginary circular loop parallel to the plates (also circular) and having the area equal to half of the area of the plates, in one time constant is:

    In the given cross-section which lies inside the capacitor plates , no charge flows. hence the required charge is 0.

    In the circuit shown the capacitor of capacitance C is initially uncharged. Now the capacitor is connected in the circuit as shown. The charge passed through an imaginary circular loop parallel to the plates (also circular) and having the area equal to half of the area of the plates, in one time constant is:

    physics-General
    In the given cross-section which lies inside the capacitor plates , no charge flows. hence the required charge is 0.