Question

A cart of mass $0.5\text{kg}$ is placed on a smooth surface and is connected by a string to a block of mass $0.2\text{kg}$. At the initial moment, the cart moves to the left along a horizontal plane at a speed of $7\text{m/s}$. Then: (Use $g=9.8{\text{m/s}}^2$ )

• A. The acceleration of the cart is $\frac{g}{7}{\text{m/s}}^2$ towards right.
• B. The acceleration of the cart is $\frac{2g}{9}{\text{m/s}}^2$ towards right.
• C. The distance travelled by the cart in the first $5\text{s}$ is $12.5\text{m}$.
• D. The speed of the cart after $5\text{s}$ will be same as initial speed.

Answer 1

The correct option is D The speed of the cart after $5\text{s}$ will be same as initial speed.

$\Rightarrow 0.2g=0.7a\Rightarrow a=\frac{2g}{7}{\text{m/s}}^2$
For the case, it comes to rest when $v=0$
$0=7+(-\frac{2gt}{7})\Rightarrow t=\frac{49}{2g}=2.5\text{s}$

Distance travelled till it comes to rest,
$0=7^2+2(-\frac{2g}{7})\text{s}$
$s=8.75\text{m}$
So in next $2.5\text{s}$, it covers $8.75\text{m}$ towards right. Total distance $=2\times 8.75=17.5\text{m}$
After $5\text{s}$, its speed will be same as that of initial $\left(7\text{m/s}\right)$ but direction will be reversed.