Question

A child of mass $30\text{kg}$ is sliding down a school slides with an angle of inclination of ${37}^{\circ }$ with horizontal. He can hold the railing on the sides of the slider in order to slide down without any acceleration. The force by the railing on the child for which he can do so is
(Given $\mu =\frac{1}{3}$ and $g=10{\text{m/s}}^2$)

• A. $50\text{N}$ along $+x$ direction
• B. $100\text{N}$ along $+x$ direction
• C. $50\text{N}$ along $-x$ direction
• D. $100\text{N}$ along $-x$ direction

Answer 1

The correct option is D $100\text{N}$ along $-x$ direction

The FBD of the figure is as shown:
force down the incline, $F$ $=30g\sin {37}^{\circ }=180\text{N}$ down the plane.
Frictional force $=\mu mg\cos {37}^{\circ }=80\text{N}$ up the plane.
Hence the unbalanced force of $100\text{N}$ is to be applied up the plane for it to move without any acceleration.