Question

When a force of $1$N acts on $1$kg mass at rest for $1$s, its final momentum is $P$. When $1$N force acts on $1$kg mass at rest through a distance $1$m, its final momentum is $P^{\prime }$. The ratio of $P$ to $P^{\prime }$ is:

• A. $1:1$
• B. $1:\sqrt{2}$
• C. $1:2$
• D. $2:1$

Answer 1

Answer: (B)

$1:\sqrt{2}$

$F=1N,t=1S$

$△P=F\times t=1N\times 1S=1kgm/s$

$P_f-P_i=1kgm/s$

$P_f-0=1kgm/s$

$P_f=1kgm/s$

$F=1N,M=1kgm,S=1m$

$a=\frac{F}{M},\frac{1N}{1Kg}=1m/s^2$

$V_f^2-V_i^2=2as$

$V_f^2-0=2\left(1m/s^2\right)\left(1m\right)$

$V_f=\sqrt{2ms}$

multiply both sides

${mv}_f=\sqrt{2m/s}\times 1kg$

$P^{\prime }=\sqrt{2}kgm/s$

$\frac{p}{p^{\prime }}=\frac{1}{\sqrt{2}}=\frac{1}{\sqrt{2}}=1:\sqrt{2}$