A body of mass m is suspended from a string o | vedclass

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

Question

(D) To complete a full vertical circle,the tension at the highest point must be at least zero $(T \ge 0)$. At the highest point,the forces acting are

Vedclass · Accepted Answer

$v = \sqrt{5gl}$

Vedclass · Answer

(D) To complete a full vertical circle,the tension at the highest point must be at least zero $(T \ge 0)$. At the highest point,the forces acting are gravity $(mg)$ and tension $(T)$,providing the centripetal force: $T + mg = \frac{mv_h^2}{l}$. Setting $T = 0$ for the minimum velocity at the top,we get $mg = \frac{mv_h^2}{l}$,which implies $v_h = \sqrt{gl}$. Using the law of conservation of energy between the lowest point (velocity $v$) and the highest point (velocity $v_h$): $\frac{1}{2}mv^2 = \frac{1}{2}mv_h^2 + mg(2l)$. Substituting $v_h^2 = gl$: $\frac{1}{2}mv^2 = \frac{1}{2}m(gl) + 2mgl = \frac{5}{2}mgl$. Solving for $v$,we get $v = \sqrt{5gl}$.

$A$ body of mass $m$ is suspended from a string of length $l$. What is the minimum horizontal velocity that should be given to the body in its lowest position so that it may complete one full revolution in a vertical plane with the point of suspension as the center of the circle?

Similar Questions

As shown in the figure, a mass $m$ and another block of mass $10m$ are connected with a string of length $L$. Friction is sufficient to prevent the slipping of the $10m$ block. Mass $m$ is given a velocity $u$ in the vertical direction. For the complete circular motion of mass $m$:

In a vertical circle of radius $r$,at what point in its path does a particle have tension equal to zero if it is just able to complete the vertical circle?

$A$ stone of mass $m$ is moving in a vertical circle of radius $20 \ cm$. What is the difference in kinetic energy between the lowest and highest points?

$A$ stone of mass $900 \,g$ is tied to a string and moved in a vertical circle of radius $1 \,m$ making $10 \,rpm$. The tension in the string, when the stone is at the lowest point is (if $\pi^2=9.8$ and $g=9.8 \,m/s^2$): (in $\,N$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module