Question

At the instant $t=0,$ a force $F=kt$ ( $k$ is a constant) acts on a small body of mass $m$ resting on a smooth horizontal surface. The time, when the body leaves the surface is

• A. $mgksin \alpha $
• B. $\frac{k \, sin \, \alpha }{m g}$
• C. $\frac{m g \, sin \alpha }{k}$
• D. $\frac{m g}{k \, sin \alpha }$

Answer 1

Answer: (D)

$N+F \, sin \alpha =mg$
The body leaves the surface when the normal reaction on it becomes zero.
$N=0$
$\Rightarrow kt \, sin \alpha =mg$
$t=\frac{m g}{k sin \alpha }$