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Question

A pulley system is attached to an elevator as shown in figure. The elevator starts to move up with an acceleration a.

Match statements in column I with results in column II.
Column IColumn II(a)Acceleration of m1 in elevator frame(p)12((m2m1)g+2m2am1+m2)t2(b)Acceleration of m1 in ground frame(q)12[m2m1(m1+m2)(g+a)]t2(c)Distance covered of m1 in elevator frame(r)(m2m1m1+m2)g+(2m2m1+m2)a(d)Distance covered of m1 in ground frame(s)(m2m1)(m1+m2)(g+a)(t)None of the above

A
a - s; b - r; c - q; d - p
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B
a - r; b - q; c - p; d - s
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C
a - s; b - t; c - q; d - t
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D
a - r; b - q; c - s; d - p
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Solution

The correct option is A a - s; b - r; c - q; d - p

Consider an observer in elevator frame,

From figure,
Tm1(a+g)=m1a1 ... (1)
m2(a+g)T=m2a1 ... (2)
From (1) and (2),
m2(a+g)m1(a+g)=(m1+m2)a1
a1=(m2m1)(a+g)(m1+m2)
Distance covered in elevator frame
=12((m2m1)(a+g)(m1+m2))×t2

In ground frame,

a1+a=m2am1a+gm2gm1+am1+m2a(m1+m2)=(m2m1m1+m2)g+(2m2m1+m2)a

Distance covered in ground frame =12((m2m1)g+2m2am1+m2)t2

(a) → (s); (b) → (r); (c) → (q); (d) → (p)

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