A small mass attached to string rotates on a frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will
Kinetic energy is the energy possessed by an object due to its motion. It is calculated using the formula KE = (1/2) mv² where m is the mass and v is the velocity. Kinetic energy increases with the square of velocity and plays a crucial role in dynamics and mechanics.
Class 11 Physics Chapter 5 Work Energy and Power covers the principles of work energy and power emphasizing their definitions and interrelationships. The chapter explores kinetic and potential energy types and the law of conservation of energy providing practical examples and mathematical formulations to enhance understanding for CBSE EXAM 2024-25.
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To find how the kinetic energy of a mass changes when the radius of its circular motion is decreased by a factor of 2 while the tension in the string is increased, we can use the following relationships:
1. The centripetal force required to keep the mass moving in a circular path is provided by the tension in the string:
T = (m * v²) / r
where T is the tension, m is the mass, v is the velocity, and r is the radius.
2. The kinetic energy (K.E.) of the mass is given by:
K.E. = (1/2) * m * v².
3. If the radius is reduced to half of the previous value (r’ = r/2) and assuming tension is increased to a level at which circular motion will be maintained, we have
T’ = (m * v’²) / (r/2)
T’ = (2 * m * v’²) / r.
4. Keeping T’ constant and solving for v’, we see that v’ must be greater to be in equilibrium.
5. Putting it all back together to find the kinetic energy:
K.E.’ = (1/2) * m * (v’)².
Since v’ = √2 * v, the kinetic energy is multiplied by a factor of 4.
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