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 percentage decrease in the weight of a rocket,when taken to a height of $32 \ km$ above the surface of the Earth,will be $.....\%$
(Radius of Earth $= 6400 \ km$)

$A$ body weighs $72 \ N$ on the surface of the earth. What is the gravitational force on it at a height equal to half the radius of the earth (in $N$)?

If the density of the earth is doubled keeping its radius constant,then the acceleration due to gravity will be........ $m/s^2$. $(g = 9.8\,m/s^2)$

The radius of the Earth is approximately $6000 \, km$. The weight of a body at a height of $6000 \, km$ from the Earth's surface becomes:

Vedclass Test Series

Exam Paper Generator

Online Exam Module