KVPY SX SB Exam 2013 Question Paper

Question : 91 of 120

Marks: +1, -0

PHYSICS

A bullet of mass m is fired horizontally into a large sphere of mass M and radius R resting on a smooth horizontal table.

The bullet hits the sphere at a height h from the table and sticks to its surface. If the sphere starts rolling without slipping immediately on impact, then

$h/R={4m+3M}/{2(m+M)}$
$h/R={m+M}/{m+2M}$
$h/R={10m+7M}/{5(m+M)}$
$h/R={4m+3M}/{m+ M}$

Validate

Solution:

Apply conservation of linear momentum

mv = (m + M) v_0

mv\sin θ\R=(2/5MR^2+mR^2)ω+0

mv({h-R}/R)R=(2M+5M)/5ω_0R^2

(m+H)(h-R)ω_0R

=(2M+5M)/5ω_0R^2

h/R={10m+7M}/{5(m+M)}

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