Question:
A block of mass ‘m’ (as shown in figure) moving with kinetic energy E compresses a spring through a distance 25 cm when its speed is halved. The value of spring constant of used spring will be nE Nm–1 for n = _______.
A block of mass ‘m’ (as shown in figure) moving with kinetic energy E compresses a spring through a distance 25 cm when its speed is halved. The value of spring constant of used spring will be nE Nm–1 for n = _______.
Updated On: Mar 19, 2025
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Correct Answer: 24
Solution and Explanation
When the velocity is halved the kinetic energy is reduced by a factor of \(\frac{1}{4}\).
ΔKE= W all So \(\frac{E}{4-E}\)=−\(\frac{1}{2}\)K×(0.25)2×\(\frac{3E}{4}\)=\(\frac{1}{2}\)K×\(\frac{1}{16}\)K=24 E
ΔKE= W all So \(\frac{E}{4-E}\)=−\(\frac{1}{2}\)K×(0.25)2×\(\frac{3E}{4}\)=\(\frac{1}{2}\)K×\(\frac{1}{16}\)K=24 E
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Concepts Used:
Center of Mass
The center of mass of a body or system of a particle is defined as a point where the whole of the mass of the body or all the masses of a set of particles appeared to be concentrated.
The formula for the Centre of Mass:
Center of Gravity
The imaginary point through which on an object or a system, the force of Gravity is acted upon is known as the Centre of Gravity of that system. Usually, it is assumed while doing mechanical problems that the gravitational field is uniform which means that the Centre of Gravity and the Centre of Mass is at the same position.