A small disc is placed on the top of a smooth | vedclass

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

Question

(B) For the disc to leave the surface of the hemisphere immediately at the top,the normal reaction $N$ between the disc and the hemisphere must be zer

Vedclass · Accepted Answer

$v = \sqrt {gR} $

Vedclass · Answer

(B) For the disc to leave the surface of the hemisphere immediately at the top,the normal reaction $N$ between the disc and the hemisphere must be zero at the highest point.At the top of the hemisphere,the forces acting on the disc are the gravitational force $mg$ acting downwards and the normal reaction $N$ acting upwards.The centripetal force required for circular motion is provided by the net radial force:$mg - N = \frac{mv^2}{R}$To leave the surface immediately,we set the normal reaction $N = 0$:$mg - 0 = \frac{mv^2}{R}$$mg = \frac{mv^2}{R}$$v^2 = gR$$v = \sqrt{gR}$Thus,the smallest horizontal velocity required is $\sqrt{gR}$.

$A$ small disc is placed on the top of a smooth hemisphere of radius $R$. What is the smallest horizontal velocity $v$ that should be given to the disc for it to leave the hemisphere immediately at the top and not slide down it? [There is no friction]

Similar Questions

$A$ stone of mass $16 \, kg$ is attached to a string $144 \, m$ long and is whirled in a horizontal circle. The maximum tension the string can withstand is $16 \, N$. The maximum velocity of revolution that can be given to the stone without breaking it will be ....... $m/s$.

$A$ cyclist goes round a circular path of circumference $34.3 \ m$ in $\sqrt{22} \ s$. The angle made by him with the vertical will be ....... $^o$.

An object of mass $m$ moves with constant speed in a circular path of radius $R$ under the action of a force of constant magnitude $F$. The kinetic energy of the object is ............

$A$ ball of mass $m$ is attached to the free end of a string of length $l$. The ball is moving in a horizontal circular path about the vertical axis as shown in the diagram. The angular velocity $\omega$ of the ball will be ($T =$ Tension in the string).

Vedclass Test Series

Exam Paper Generator

Online Exam Module