A weightless thread can support tension upto 30 ,N . A stone of mass 0.5 ,kg is tied to it and is re

English

Gujarati

Hindi

5.Work, Energy, Power and Collision

medium

A weightless thread can support tension upto $30 \,N$. 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 $g = 10m/{s^2}$, then the maximum angular velocity of the stone will be ........ $rad/s$

A

$5$

B

$\sqrt {30}$

C

$\sqrt {60}$

D

$10$

Solution

(a) ${T_{\max }} = m\omega _{^{\max }}^2r + mg$

$⇒$ $\frac{{{T_{\max }}}}{m} = {\omega ^2}r + g$

$⇒$ $\frac{{30}}{{0.5}} – 10 = {\omega ^2}_{\max }r$

$⇒$ ${\omega _{\max }} = \sqrt {\frac{{50}}{r}} = \sqrt {\frac{{50}}{2}} = 5\,rad/s$

Standard 11

Physics

Share

Similar Questions

$A$ small ball $B$ of mass $m$ is suspended with light inelastic string of length $L$ from $a$ block $A$ of same mass $m$ which can move on smooth horizontal surface as shown in the figure. The ball is displaced by angle $\theta$ from equilibrium position & then released. The displacement of block when ball reaches the equilibrium position is

hard

A ball is moving to and fro about the lowest point $A$ of a smooth hemispherical bowl. If it is able to rise up to a height of $20 \,cm$ on either side of $A$, its speed at $A$ must be ………. $m/s$ (Take = $10 m/s^2$, mass of the body $5 \,g$)

medium

A weightless thread can bear a tension upto $3.7\,kg-wt$ . A stone of mass $500\,g$ is tied to it and revolved in a circular path of radius $4\,m$ in a vertical plane. If $g = 10\,ms^{-2}$, then the maximum angular velocity of the stone will be ……… $rad\,s^{-1}$

medium

A particle of mass $m$ is tied to one end of $a$ string of length $l$. The particle is held horizontal with the string $mg$ taut. It is then projected upward with $a$ velocity $u$. The tension in the string is $\frac{{mg}}{2}$ when it is inclined at an angle $30^o$ to the horizontal. The value of $u$ is

hard

A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from $A$ to $B$, the force it applies on the wire is

medium