Question

A block is placed on a rough horizontal plane. A time dependent horizontal force F = Kt acts on the block. Here, K is positive constant. Acceleration - time graph of the block is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Block starts sliding over the surface when, F = max force of friction
or $Kt=\mu \text{mg}$
or $t=\frac{\mu mg}{K}$
For $t>\frac{\mu mg}{K}$
net acceleration of block is,
$a=\frac{F-\mu mg}{m}=\frac{Kt}{m}-\mu g$
Which is a straight line with positive slope and negative
intercept. So, for $t\le \frac{\mu mg}{K}$, acceleration of the particle is zero and for $t>\frac{\mu mg}{K}$, acceleration is $a=\frac{Kt}{m}-\mu g$
Hence, the correct answer is option (c)