What is the minimum velocity with which a bod | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) To complete a vertical loop,the body must maintain a minimum velocity at the highest point $C$ such that the tension $T_C$ in the string (or norma

Vedclass · Accepted Answer

$\sqrt{5gR}$

Vedclass · Answer

(B) To complete a vertical loop,the body must maintain a minimum velocity at the highest point $C$ such that the tension $T_C$ in the string (or normal force) is at least zero.At the highest point $C$,the forces acting on the body are gravity $(mg)$ acting downwards and tension $(T_C)$ acting downwards. The centripetal force is provided by the sum of these forces:$T_C + mg = \frac{mv_C^2}{R}$For the minimum velocity,we set $T_C = 0$,which gives:$mg = \frac{mv_C^2}{R} \Rightarrow v_C = \sqrt{gR}$Now,we apply the law of conservation of mechanical energy between the lowest point $A$ and the highest point $C$. Let $v_0$ be the velocity at point $A$:Total Energy at $A$ = Total Energy at $C$$\frac{1}{2}mv_0^2 = \frac{1}{2}mv_C^2 + mg(2R)$Substituting $v_C^2 = gR$:$\frac{1}{2}mv_0^2 = \frac{1}{2}m(gR) + 2mgR$$\frac{1}{2}mv_0^2 = \frac{5}{2}mgR$$v_0^2 = 5gR$$v_0 = \sqrt{5gR}$

What is the minimum velocity with which a body of mass $m$ must enter a vertical loop of radius $R$ so that it can complete the loop $?$

Similar Questions

$A$ weightless thread can support a tension of up to $30 \, N$. $A$ stone of mass $0.5 \, kg$ is tied to it and is revolved in a circular path of radius $2 \, m$ in a vertical plane. If $g = 10 \, m/s^2$,then the maximum angular velocity of the stone will be ........ $rad/s$.

$A$ body crosses the topmost point of a vertical circle with critical speed. Its centripetal acceleration,when the string is horizontal,will be $....g$

$A$ ball of mass $2 \,g$ released from the top of an inclined plane describes a circular motion of radius $20 \,cm$ in the vertical plane upon reaching the bottom. The minimum height of the inclined plane is (in $\,cm$)

$A$ bucket tied at the end of a $1.6\, m$ long string is whirled in a vertical circle with constant speed. What should be the minimum speed so that the water from the bucket does not spill,when the bucket is at the highest position? (Take $g = 10\, m/s^2$)

The minimum velocity $v$ required for a simple pendulum to complete one full rotation in a vertical plane is given. If the length of the string is reduced to one-fourth,what will be the new required velocity?

Vedclass Test Series

Exam Paper Generator

Online Exam Module