(D) The tension in the string provides the necessary centripetal force for circular motion.Initially,the tension $T_0$ is given by $T_0 = mR\omega_0^2

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(D) The tension in the string provides the necessary centripetal force for circular motion.Initially,the tension $T_0$ is given by $T_0 = mR\omega_0^2$,where $m$ is the mass,$R$ is the initial length of the string,and $\omega_0$ is the initial angular velocity.In the second case,the new length $R' = 2R$ and the new angular velocity $\omega' = 2\omega_0$.The new tension $T$ is given by $T = mR'(\omega')^2$.Substituting the new values: $T = m(2R)(2\omega_0)^2 = m(2R)(4\omega_0^2) = 8mR\omega_0^2$.Since $T_0 = mR\omega_0^2$,we have $T = 8T_0$.

Class 11 Physics 3-2.Motion in Plane Dynamics of circular Motion (Centrifugal force) and Pendulum and Motion on Curved path

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$A$ mass is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity $\omega_0$. If the length of the string and angular velocity are doubled,the tension in the string which was initially $T_0$ is now

AIIMS 1985 All AIIMS

A
$T_0$
B
$T_0/2$
C
$4T_0$
D
$8T_0$

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3-2.Motion in Plane

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Dynamics of circular Motion (Centrifugal force) and Pendulum and Motion on Curved path

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$A$ mass is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity $\omega_0$. If the length of the string and angular velocity are doubled,the tension in the string which was initially $T_0$ is now

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