A hemispherical bowl of radius R is rotated a | vedclass

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

Question

(A) The forces acting on the block are the normal force $N$ and the gravitational force $mg$. The block moves in a horizontal circle of radius $x = R

Vedclass · Accepted Answer

$\cos^{-1}\left(\frac{g}{R\omega^2}\right)$

Vedclass · Answer

(A) The forces acting on the block are the normal force $N$ and the gravitational force $mg$. The block moves in a horizontal circle of radius $x = R \sin 	heta$.For the vertical direction,the forces are balanced:$N \cos 	heta = mg$  ......$(i)$For the horizontal direction,the normal force provides the necessary centripetal force:$N \sin 	heta = m x \omega^2 = m (R \sin 	heta) \omega^2$  ......(ii)Dividing equation (ii) by equation $(i)$:$\frac{N \sin 	heta}{N \cos 	heta} = \frac{m R \sin 	heta \omega^2}{mg}$$	an 	heta = \frac{R \sin 	heta \omega^2}{g}$Since $	an 	heta = \frac{\sin 	heta}{\cos 	heta}$,we have:$\frac{\sin 	heta}{\cos 	heta} = \frac{R \sin 	heta \omega^2}{g}$$\frac{1}{\cos 	heta} = \frac{R \omega^2}{g}$$\cos 	heta = \frac{g}{R \omega^2}$$	heta = \cos^{-1}\left(\frac{g}{R \omega^2}ight)$

Similar Questions

$A$ stone of mass $0.3\,kg$ attached to a $1.5\,m$ long string is whirled around in a horizontal circle at a speed of $6\,m s^{-1}$. The tension in the string is $............\,N$.

An aircraft executes a horizontal loop at a speed of $720 \; km/h$ with its wings banked at $15^{\circ}$. What is the radius of the loop in $km$?

$A$ train is running at $20 \, m/s$ on a railway line with a radius of curvature of $40,000 \, m$. The distance between the two rails is $1.5 \, m$. For safe running of the train,the elevation of the outer rail over the inner rail is ...... $mm$ $(g = 10 \, m/s^2)$.

With what frequency should a particle of mass $m$ be rotated so that a body of mass $M$ remains stationary?

$A$ 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 ....... $^o$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module