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qUESTIONS

Three Carnot engines operate in series between a heat source at a temperature T₁ and a heat sink at temperature T4 (see figure). There are two other reservoirs at temperature T₂ and T3 as shown, with T₁ >T₂ >T3 >T4. The three engines are equally efficient if

A body of mass 1kg falls freely from a height of 100m, on a platform of mass 3 kg which is mounted on a spring having spring constant k = 1.25×106 N/m . The body sticks to the platform and the spring’s maximum compression in found to be x. Given that g = 10 ms-2 the value of x will be close to

The period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination a, is given by

A simple pendulum has time period T1. The point of suspension is now moved upward according to equation y = kt² where k = 1m/s². If new time period is 2 T2 then ratio T1^2/T2^2 will be

A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to TM . If the Young’s modulus of the material of the wire is Y then (g = gravitational acceleration) 1/Y is equal to

A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes S.H.M. of time period T. If the mass is increased by m, the time period becomes 5T/3. Then the ratio of m/M is

The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is

A mass m is suspended separately by two different springs of spring constant K1 and K2 gives the time-period t₁ and t2 respectively. If same mass m is connected by both springs as shown in figure, then time-period t is given by the relation

The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is to in air. Neglecting frictional force of water and given that the density of the bob is (4/3) ×1000 kg/m³. What relationship between t and to is true

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and the cylinder have equal cross-sectional area A. When the piston is in equilibrium, the volume of the gas is V0 and its pressure is P0 The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency

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