Question

The rear side of a truck is open and a box of mass $2$kg is placed on the truck $8$m away from the open end. The truck starts from rest with an acceleration of $2m/s^2$ on a straight road. The box will fall off the truck when it is at distance from the starting point equal to(Given, $\mu =0.1$ and $g=10m/s^2$).

• A. $4$m
• B. $8$m
• C. $12$m
• D. $16$m

Answer 1

The correct option is D $16$m

Let a be the acceleration of truck.
$ma-\mu mg=m{a}_0$
$a_0=a-\mu g$
$=2-0.1\times 10=1m/s^2$
$8=\frac{1}{2}{a}_0{t}^2$
$=\frac{1}{2}\times 1\times t^2$
$\Rightarrow t=4$s
The block will fall off the truck after $4$s.
For truck,
Distance travelled by the truck in this time.
$S=\frac{1}{2}a{t}^2=\frac{1}{2}\times 2\times 4^2=16$m.