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Question: A bullet weighing \(10g\) and moving at \(300m/s\) strikes a \(5kg\) ice and drops dead. The ice blo...

A bullet weighing 10g10g and moving at 300m/s300m/s strikes a 5kg5kg ice and drops dead. The ice block is sitting on a frictionless level surface. The speed of the block after the collision is
A. 6cm/s{\text{6cm/s}}
B. 6m/s{\text{6m/s}}
C. 60cm/s{\text{60cm/s}}
D. 60m/s{\text{60m/s}}

Explanation

Solution

First convert all the units of the given terms in the same system of units. Here use the basic law for the conservation of momentum and the velocity. Momentum in an isolated system remains constant. The law of the momentum states that momentum can never be created nor destroyed. It states that momentum of an object before collision and after collision remains the constant.

Complete step by step answer:
Let us suppose that mass be m1=10g=10×10−3kg{m_1} = 10g = 10 \times {10^{ - 3}}kg
Velocity of the bullet be v1=300m/s{v_1} = 300m/s
Velocity of the ice is v2=0m/s{v_2} = 0m/s
Mass of the ice, is m2=5kg{m_2} = 5kg
In any isolated system, the total momentum of any object before the collision is equal to the total momentum after the collision.
Given that - A bullet weighing 10g10g and moving at 300m/s300m/s strikes a 5kg5kg ice and drops dead
m1v1+m2v2=m2v{m_1}{v_1} + {m_2}{v_2} = {m_2}v
Place the known values in the above equation –
10×10−3(300)+5(0)=5v10 \times {10^{ - 3}}(300) + 5(0) = 5v
Simplify the above equation and make unknown “v” the subject –
3000 \times {10^{ - 3}} = 5v \\\
\implies 3 = 5v \\\
\implies v = \dfrac{3}{5} \\\
∴v=0.6m/s \therefore v = 0.6m/s \\\
Therefore, the speed of the block after the collision is 0.6m/s=0.6×100cm/s=60cm/s0.6m/s = 0.6 \times 100cm/s = 60cm/s

So, the correct answer is “Option C”.

Note:
The law of momentum is applicable to all the interactions, collisions caused by the explosive forces and applicable to all the systems no matter how complicated the force is between the particles. It can also be used and applicable where Newton’s laws do not hold. Remember all the basic laws to solve these types of equations.