Question

A disc of mass 10 g is kept floating horizontally in
air by firing bullets, each of mass 5 g, with the same
upward velocity and at a rate of 10 bullets per
second. The bullets rebound with the same speed in
opposite direction. The velocity of each bullet at the
time of impact is
(1) 196 cm s-
(2) 98 cm s-
(3) 49 cm s?
(4) 392 cm -​

Answer 1

Given:

A disc of mass 10 g is kept floating horizontally in

air by firing bullets, each of mass 5 g, with the same upward velocity and at a rate of 10 bullets/s The bullets rebound with the same speed in

opposite direction.

To find:

Velocity of bullets at the time of impact.

Calculation:

The force exerted by "Momentum change" of bullets is equal and opposite to the weight of the disc exerted by the gravity.

Let velocity at time of impact be v:

$\rm{ \therefore \: weight = bullet \: force}$

$\rm{ = > Mg = \{mv - ( - mv) \} \times n}$

$\rm{ = > Mg = \{2 mv \} \times n}$

$\rm{ = > {10}^{ - 2} \times 9.8 = \{2 \times 5 \times {10}^{ - 3} \times v \} \times 10}$

$\rm{ = > {10}^{ - 2} \times 9.8 = {10}^{ - 1} \times v }$

$\rm{ = > {10}^{ - 1} \times 9.8 = v }$

$\rm{ = > v = 98 \times {10}^{ - 2} \: m {s}^{ - 1} }$

$\rm{ = > v = 98 \: cm {s}^{ - 1} }$

So, final answer is :

$\boxed{ \blue{ \sf{ v = 98 \: cm {s}^{ - 1} }}}$