A bob attached to a string is held horizontal | vedclass

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

Question

(A) Let the length of the string be $L$. When the bob is at a vertical distance $h$ below the point of suspension,the angle $	heta$ with the vertical

Vedclass · Accepted Answer

Vedclass · Answer

(A) Let the length of the string be $L$. When the bob is at a vertical distance $h$ below the point of suspension,the angle $	heta$ with the vertical is given by $\cos 	heta = \frac{h}{L}$.Using the conservation of energy from the horizontal position (where $h=0$) to a position at depth $h$,the kinetic energy is $mgh = \frac{1}{2}mv^2$,so $v^2 = 2gh$.The forces acting on the bob are tension $T$ towards the center and the component of gravity $mg \cos 	heta$ away from the center. The net centripetal force is $T - mg \cos 	heta = \frac{mv^2}{L}$.Substituting $v^2 = 2gh$ and $\cos 	heta = \frac{h}{L}$:$T = \frac{m(2gh)}{L} + mg \left(\frac{h}{L}ight) = \frac{2mgh}{L} + \frac{mgh}{L} = \frac{3mgh}{L}$.Since $T = \left(\frac{3mg}{L}ight)h$,the relationship between $T$ and $h$ is linear,passing through the origin. This corresponds to the graph where $T$ increases linearly with $h$.

$A$ bob attached to a string is held horizontal and released. The tension $T$ and vertical distance $h$ from the point of suspension can be represented by which of the following graphs?

Similar Questions

$A$ particle is rotated in a vertical circle by connecting it to a light rod of length $l$ and keeping the other end of the rod fixed. The minimum speed of the particle when the light rod is horizontal for which the particle will complete the circle is

$A$ body of mass $m$ is tied to a string of length $l$ and rotated in a vertical circle. What is the difference in tension between the lowest point and the highest point (in $,mg$)?

$A$ $2 \, kg$ mass is attached to a string of length $1 \, m$ and is whirled in a vertical circle at a constant speed of $5 \, m/s$. At what position will the tension in the string be $70 \, N$? $(g = 10 \, m/s^2)$.

$A$ bullet of mass $m$ moving with velocity $v$ passes through a pendulum bob of mass $M$ and emerges with a velocity $v/2$. What is the minimum value of $v$ so that the pendulum bob completes a full vertical circle of length $\ell$?

$A$ mass $m$ is released from point $A$ as shown in the figure. The tension in the string at point $B$ will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module