Consider a particle of mass m suspended by a | vedclass

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

Question

(D) When a body is suspended by a string at a position $P$ with latitude $\lambda$,the body rotates with the angular velocity $\omega$ of the Earth. T

Vedclass · Accepted Answer

$\frac{G M m}{R^2}-m \omega^2 R$

Vedclass · Answer

(D) When a body is suspended by a string at a position $P$ with latitude $\lambda$,the body rotates with the angular velocity $\omega$ of the Earth. The effective force acting on the body is the gravitational force minus the centripetal force required for circular motion.The tension $T$ in the string is given by:$T = mg - mr\omega^2 \cos \lambda$Since $g = \frac{GM}{R^2}$ and the radius of the circular path at latitude $\lambda$ is $r = R \cos \lambda$,we substitute these into the equation:$T = m \left( \frac{GM}{R^2} \right) - m(R \cos \lambda) \omega^2 \cos \lambda$$T = \frac{GMm}{R^2} - mR\omega^2 \cos^2 \lambda$At the equator,the latitude $\lambda = 0^{\circ}$.Substituting $\lambda = 0^{\circ}$ and $\cos 0^{\circ} = 1$:$T = \frac{GMm}{R^2} - mR\omega^2 (1)^2$$T = \frac{GMm}{R^2} - mR\omega^2$

Consider a particle of mass $m$ suspended by a string at the equator. Let $R$ and $M$ denote the radius and mass of the Earth. If $\omega$ is the angular velocity of rotation of the Earth about its own axis,then the tension on the string will be $(\cos 0^{\circ}=1)$

Similar Questions

The rotation of the Earth (of radius $R$) about its axis speeds up to a value such that a man at latitude angle $45^{\circ}$ feels weightlessness. The duration of a day in such a case is

The value of acceleration due to gravity at a height of $4 R_E$ from the surface of the Earth is (where $R_E$ is the radius of the Earth and acceleration due to gravity on the surface of the Earth $g = 10 \,ms^{-2}$): (in $\,ms^{-2}$)

The height at which the weight of a body becomes $\frac{1}{16}^{th}$ of its weight on the surface of the Earth (radius $R$) is: (in $R$)

$A$ tunnel is dug along a diameter of the Earth. If $M_e$ and $R_e$ are the mass and radius of the Earth respectively,then the force on a particle of mass $m$ placed in the tunnel at a distance $r$ from the center is:

If $R$ is the radius of the earth and $g$ is the acceleration due to gravity on the earth's surface,the mean density of the earth is

Vedclass Test Series

Exam Paper Generator

Online Exam Module