Question

A small block of mass m slides along a smooth frictional track as shown in the figure. (i) If it starts from rest at P, what is the resultant force acting on it at Q? (ii) At what height above the bottom of the loop should the block be released so that the force it exerts against the track at the top of the loop equals its weight-

• A. $\sqrt{75}$mg, 3R
• B. $\sqrt{65}$mg, 2R
• C. $\sqrt{75}$mg, 2R
• D. $\sqrt{65}$mg, 3R

Answer 1

Answer: (D)

$\sqrt{65}$mg, 3R

Answer 2

From energy conservation,

Mg(4R) = $\frac{1}{2}$mv² ̃ v = $\sqrt{8Rg}$

At q, N = $\frac{mv^{2}}{R}$ ̃ N = $\frac{m}{R}$×8gR = 8mg

So net force at q, F_net= $\sqrt{N^{2} + (mg)^{2}}$=$\sqrt{65}$mg