Question

A 10 kg block is pulled a along a frictional surface in the form of an are of a circle of radius 10 m. The applied force F is 200 N as shown in figure If a block started from rest at P

• A. the velocity at Q would be 20 m/s
• B. the velocity at Q would be 17 m/s
• C. the velocity at Q would be 15 .5 m.s
• D. the velocity at Q would be 18 m/s

Answer 1

The correct option is A the velocity at Q would be 20 m/s

We know,

change in KE $=$ work done

$(KE{)}_f-(KE{)}_i=F$(length of arc)

$(KE{)}_f-O=F\times {60}^o\times \frac{\pi }{{80}^o}\times$ (radius) [Initially at rest]

$(KE{)}_f=\frac{\pi F}{3}\times 10$

$(KE{)}_f=\frac{\pi \times 200}{3}\times 10$

$\frac{1}{2}m{v}_f^2=\frac{2000\pi }{3}$

$v_f^2=\frac{2}{m}\times \frac{2000\pi }{3}$

$v_f=\sqrt{\frac{2}{10}\times \frac{2000\pi }{3}}$

$v_f\approx 20m/s$,