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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
A)A simple pendulum of length 'l' oscillating with small amplitude in a lift moving down with retardation g/2.P)T=2π2l3g
B)A block attached to an end of a vertical spring, whose other end is fixed to the ceiling of a lift, stretches the spring by length 'l' in equilibrium. It's time period when lift moves up with an acceleration g/2 isQ)T=2πlg
C)The time period of small oscillation of a uniform rod of length 'l' smoothly hinged at one end. The rod oscillates in vertical plane.R)T=2π2lg
D)A cubical block of edge 'l' and specific density ρ2 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 isS)T=2πl2g

 

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a

A– Q, B– R, C– S, D–P

b

A – P, B – Q, C – P, D – S 

c

A – S, B – R, C – S, D – P

d

A – S, B – P, C – Q, D – R 

answer is D.

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Detailed Solution

(A) In frame of lift effective acceleration due to gravity is g+g2=3g2 downwards  T=2π2l3g

(B) Kl = mg 

km=gL

Constant acceleration of lift has no effect in time period of oscillation. 

T=2πmk=2πlg

(C) T=2πImgd=2πml23mgl2=2π2l3g

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