Question

A 50 g bullet moving with velocity 10 m/s strikes a block of mass 950 g at rest and gets embedded in it. The loss in kinetic energy will be
(A) 100%
(B) 95%
(C) 5%
(D) 50%

Answer 1

Hint
The kinetic energy (KE) of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes.

Complete step by step answer
According to the question given that velocity of the bullet is 10 m/s, block mass is 950 g. and the mass of the bullet is 50 g.
By conservation of momentum
final velocity of embedded body = mass of bullet × velocity of bullet ÷ mass of bullet + mass of stationary body
initial kinetic energy (According to the formula) = $\dfrac{1}{2}m{v^2}$
∴ initial kinetic energy = $\dfrac{1}{2} \times 50 \times {10^2} = 2500J$
Same as, final kinetic energy is $\dfrac{1}{2} \times 950 \times {10^2} = 47500J$
The loss of kinetic energy = final K.E – initial K.E
So, the loss of kinetic energy is = $\dfrac{{2500}}{4} = 100\%$
Option (A) is correct.

Note
Velocity is defined as the rate change of displacement per unit time. Speed in a specific direction is also known as velocity. Velocity is equal to displacement divided by time. velocity describes the motion of objects. Velocity measures the movement of objects based on their speed and direction. ... Speed is a scalar measurement since it only defines the magnitude of how fast an object is moving. Velocity is a vector quantity since it describes both speed and direction.