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Conservation of energy

pendulum
2022, Class 11, Conservation of energy, Mains, Work, Energy, and Power

The pendulum is suspended by a string a length 250 cm. The bob has a mass of 200 g and is displaced sideways such that the string makes an angle of 60° with the vertical, as illustrated. Upon releasing the bob from this position, determine the maximum speed (in m/s) it achieves during its motion.

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student skates
2020, Advanced, Class 11, Conservation of energy, JEE, Work, Energy, and Power

A student skates up a ramp that makes an angle of 30° with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed v₀ and wants to turn around over a semicircular path xyz of radius R, during which he/she reaches a maximum height h (at point y) from the ground, as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then (g is the acceleration due to gravity)

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