The mass of the bob of a simple pendulum of l | vedclass

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

Question

(A) Let the horizontal position be the reference level for potential energy $(PE = 0)$.At the horizontal position,the total energy is $E_i = PE + KE =

Vedclass · Accepted Answer

$\sqrt{2gL}$ and $3mg$

Vedclass · Answer

(A) Let the horizontal position be the reference level for potential energy $(PE = 0)$.At the horizontal position,the total energy is $E_i = PE + KE = 0 + 0 = 0$.At the lowest position,the bob is at a vertical distance $L$ below the reference level,so its potential energy is $PE_f = -mgL$.Let the speed at the lowest position be $v$. The kinetic energy is $KE_f = \frac{1}{2}mv^2$.By the law of conservation of energy,$E_i = E_f$:$0 = -mgL + \frac{1}{2}mv^2$$mgL = \frac{1}{2}mv^2$$v^2 = 2gL \Rightarrow v = \sqrt{2gL}$.At the lowest position,the forces acting on the bob are the tension $T$ upwards and weight $mg$ downwards. The net centripetal force is:$T - mg = \frac{mv^2}{L}$Substituting $v^2 = 2gL$:$T - mg = \frac{m(2gL)}{L} = 2mg$$T = 2mg + mg = 3mg$.Thus,the speed is $\sqrt{2gL}$ and the tension is $3mg$.

The mass of the bob of a simple pendulum of length $L$ is $m$. If the bob is released from its horizontal position,then the speed of the bob and the tension in the thread at the lowest position of the bob will be respectively:

Similar Questions

$A$ frictionless track $ABCDE$ ends in a circular loop of radius $R$. $A$ body slides down the track from point $A$ which is at a height $h = 5\, cm$. The maximum value of $R$ for the body to successfully complete the loop is ........... $cm$.

$A$ stone of mass $1 \ kg$ is tied to a string $2 \ m$ long and is rotated at a constant speed of $40 \ ms^{-1}$ in a vertical circle. The ratio of the tension at the top and the bottom is [Take $g = 10 \ ms^{-2}$].

As per the given figure,to complete the circular loop,what should be the radius if the initial height is $5 \, m$ (in $, m$)?

$A$ body of mass $1\, kg$ is moving in a vertical circular path of radius $1\, m$. The difference between the kinetic energies at its highest and lowest position is ......... $J$.

$A$ 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?

Vedclass Test Series

Exam Paper Generator

Online Exam Module