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Q.

In the column-I, a system is described in each option and corresponding time period is given in the column-II. Suitably match them.

 Column-I Column-II
PA simple pendulum of length 'l' oscillating with small amplitude in a lift moving down with retardation g/2.1T=2π2l3g
QA block attached to an end of a vertical spring, whose other end is fixed to the ceiling of a stationary lift, stretches the spring by length 'l' in equilibrium. It's time period when lift moves up with an acceleration g/2 is2T=2πlg
RThe time period of small oscillation of a uniform rod of length 'l' smoothly hinged at one end. The rod oscillates in vertical plane.3T=2π2lg
SA cubical block of edge ' l ' and specific gravity 1/2 is in equilibrium with some volume inside water filled in a large fixed container. Neglect viscous forces and surface tension. The time period of small oscillations of the block in vertical direction is4T=2πl2g

 

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a

P2,Q1,R1,S  4

b

P1,Q  2,R  1,  S  3

c

P1,Q  2,R1,S  4

d

P  1,Q  2,R3,S  4

answer is B.

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Detailed Solution

A simple pendulum of length 'l' oscillating with small amplitude in a lift moving down with retardation g/2. is T=2π2l3g.

A block attached to an end of a vertical spring, whose other end is fixed to the ceiling of a stationary lift, stretches the spring by length 'l' in equilibrium. It's time period when lift moves up with an acceleration g/2 is T=2πlg.

The time period of small oscillation of a uniform rod of length 'l' smoothly hinged at one end. The rod oscillates in vertical plane is T=2π2l3g.

A cubical block of edge ' l ' and specific gravity 1/2 is in equilibrium with some volume inside water filled in a large, fixed container. Neglect viscous forces and surface tension. The time period of small oscillations of the block in vertical direction is T=2πl2g.

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