JEE Main · 2021 · 26 Feb 2021 · Shift 2 · Laws of Motion

Two masses

A

and

B

, each of mass

M

are fixed together by a massless spring. A force acts on the mass B as shown in figure. If the mass

A

starts moving away from mass

B

with acceleration '

a

', then the acceleration of mass

B

will be:

(A) $\frac{Ma - F}{M}$
(B) $\frac{M F}{F + M a}$
(C) $\frac{F + M a}{M}$ ✓ Correct
(D) $\frac{F - Ma}{M}$

Answer: (C)

Solution

When mass A moves away from B with acceleration

a

, the spring must be in tension with force

T = M a

(from Newton's second law on A). For mass B, the net force is

F

(applied) plus

T

(spring tension pulling it forward):

F + M a = M a_{B}

. Therefore,

a_{B} = \frac{F + M a}{M}

JEE Main · 2021 · 26 Feb 2021 · Shift 2 · Single correct option

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