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A spherical body of mass M ,radius R fall in a medium of viscosity K ,the time in which velocity of body increase from 0 to 0.63times the terminal velocity V is called time constant .expression of time constant T is?
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A spherical body of mass M ,radius R fall in a medium of viscosity K ,...
The time constant T of a spherical body of mass M and radius R falling in a medium of viscosity K, in which the velocity of the body increases from 0 to 0.63 times the terminal velocity V, is given by the following expression:

T = 2πMR / KV

In this expression, T is the time constant, M is the mass of the spherical body, R is the radius of the spherical body, K is the viscosity of the medium, and V is the terminal velocity of the body. The time constant represents the time it takes for the velocity of the body to reach 63% of its terminal velocity.

This expression is derived from the equation of motion for the spherical body, which takes into account the forces acting on the body, including the force of gravity, the force of drag due to the medium, and the force of buoyancy due to the medium. The time constant is an important parameter in understanding the dynamics of the body's motion, as it determines the rate at which the body accelerates and reaches its terminal velocity.
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A spherical body of mass M ,radius R fall in a medium of viscosity K ,the time in which velocity of body increase from 0 to 0.63times the terminal velocity V is called time constant .expression of time constant T is?
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