A body A of mass M while falling vertically downwards under gravity breaks into two parts; a body B of mass $1 / 3 \mathrm{M}$ and a body C of mass $2 / 3 \mathrm{M}$. The centre of mass of bodies B and C taken together shifts compared to that of body A towards

(A) depends on height of breaking

JEE Main · 2005 · 08 May 2005 · Offline · Conservation of Momentum

A body A of mass M while falling vertically downwards under gravity breaks into two parts; a body B of mass

1/3 M

and a body C of mass

2/3 M

. The centre of mass of bodies B and C taken together shifts compared to that of body A towards

(A)depends on height of breaking
(B)does not shift✓ Correct
(C)body C
(D)body B

Answer: (B)

Solution

The only external force on the body during and after the break-up is gravity, which acts on the centre of mass exactly as before. The break-up itself involves only internal forces between the fragments, so the combined centre of mass of

B

and

C

continues along the very same vertical path that

A

was following; it does not shift relative to the original body.

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option

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