Question

Which of the following will have the greatest value momentum amongst them?

• A. A $600g$ ball moving with a speed of $18m{s}^{-1}$.
• B. A $15kg$ cycle moving with a speed of $0.8m{s}^{-1}$.
• C. An idle rock of mass $3kg$.
• D. A body of mass $5kg$ moving with a speed of $1.5m{s}^{-1}$

Answer 1

The correct option is B A $15kg$ cycle moving with a speed of $0.8m{s}^{-1}$.

As it is known that
$Momentum\left(P\right)=mass\left(m\right)\times velocity\left(v\right)$

Case I: Let the mass of ball, $m_b=600g=0.6kg$ and velocity of ball, $v_b=18m{s}^{-1}$, then:
momentum of ball, $P_b=0.6\times 18=10.8kgm{s}^{-1}$.

Case II: Let the mass of cycle, $m_c=15kg$ and velocity of cycle, $v_c=0.8m{s}^{-1}$, then:
momentum of cycle, $P_c=15\times 0.8=12kgm{s}^{-1}$.

Case III: As the velocity of rock is zero, its momentum will be zero.

Case IV: Mass of the body = $5kg$
Speed of the body = $1.5m{s}^{-1}$
Momentum = $5\times 1.5=7.5kgm{s}^{-1}$

Therefore out of the given cases, the cycle will have the greatest momentum.