A $50 \mathrm{kg}$ person stands on a $25\mathrm{ }\mathrm{kg}$ platform. He pulls on the rope which is attached to the platform via the frictionless pulleys, as shown in the figure. The platform moves upward at a steady rate if the force with which the person pulls the rope is

A particle of mass $m$ is at rest at the origin at time $t=0$. It is subjected to a force $F\left(t\right)=F_0{e}^{–\mathrm{bt}}$ in the $x$-direction. Its speed $v\left(t\right)$ is depicted by which of the following curves?

A hemisphere of mass $3 \mathrm{m}$ and radius $R$ is free to slide with its base on a smooth horizontal table. A particle of mass $m$ is placed on the top of the hemisphere. If the particle is displaced with a negligible velocity, then find the angular velocity of the particle relative to the centre of the hemisphere at an angular displacement $\mathrm{\theta },$ when the velocity of the hemisphere is $v$.

A block of mass $m$ is held fixed against a wall by applying a horizontal force $F$. Which one of the following options is incorrect.

A block of mass $10 \mathrm{kg}$is suspended through two light spring balances as shown in the figure.