Question

A $10-kg$ block is pulled in the vertical plane along a frictionless surface in the form of an arc of a circle of radius $10m$.The applied force is $200N$ as shown in the figure.If the block started from rest at $A$,the velocity at $B$ would be

• A. $1.732m/s$
• B. $17.32m/s$
• C. $173.2m/s$
• D. none of these

Answer 1

Answer: (B)

$17.32m/s$

Here, $F$ is the external force, which results in tension $T=F$, along the direction of motion of the block, i.e. tangential to the circle.

Thus, Work done by $F$ from A to B is $W=F\times \frac{\pi R}{3}=200\times \frac{\pi \times 10}{3}=2094J$

Let the velocity of block at B as $v$.

Taking A as point of reference for potential energy calculations,

Initial mechanical energy at point A is, $E_A=0$

Final mechanical energy at point B is, $E_B=mgR(1-cos{60}^0)+\frac{1}{2}m{v}^2$

$⟹E_B=10\times 10\times 10(1-0.5)+\frac{1}{2}\times 10\times v^2$

$⟹E_B=500+5v^2$

As work done by external force equals change in Mechanical Energy.

$⟹W=E_B-E_A⟹5v^2=1594⟹v=17.85m/s$

Nearest option is B