A block of mass 18.5 kg kept on a smooth horizontal surface is pulled by a rope of 3 m length by a…
A block of mass 18.5 kg kept on a smooth horizontal surface is pulled by a rope of 3 m length by a horizontal force of 40 N applied to the other end of the rope. If the linear density of the rope is $0.5 \mathrm{kgm}^{-1}$ and initially the block is at rest. The time in which the block moves a distance of 9 m is
3s
5s
7s
9s
Solution
$\mathrm{M}=18.5 \mathrm{~kg}, \mathrm{~F}=40 \mathrm{~N}$
$\mu=0.5 \mathrm{~kg} \mathrm{~m}^{-1}$
Acceleration of the block-rope system is
$a=\frac{F}{M+\mu \times 3}=\frac{40}{18.5+0.5 \times 3}=2 \mathrm{~ms}^{-2}$
Time to travel the block through distance S is
$t=\sqrt{\frac{2 s}{a}}=\sqrt{\frac{2 \times 9}{2}}=3 \mathrm{~s}$
