Question

A trolley of mass 8 kg is standing on a frictionless surface inside which an object of mass 2 kg is suspended. A constant force F starts acting on the trolley as a result of which the string stood at an angle of ${37}^0$ from the vertical then.

• A. acceleration of the trolley is 40 /3 ${\sec }^2$
• B. force applied is 60 N
• C. force applied is 75 N
• D. tension in the string is 25 N

Answer 1

The correct option is C force applied is 75 N

We know that the angle made by string is $\theta =ta{n}^{-1}\left(\frac{a}{g}\right)$

where $a$ is the $acceleration$ of the frame in which the string is hanging in our case it is a $trolley.$

putting $\theta ={37}^0$ or $tan{37}^0=\frac{3}{4}$

we get $a=\frac{3g}{4}=30/4=7.5m/s^2$

Force $F=\text{total mass of the system on which force is acting}\times \text{acceleration of the system}=(8+2)\times 7.5=75$

so force is $75N$