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QJEEAdv21Phb07a: JEE Advanced 2021 Physics - Class 11 JEEAdv21Phb07a Solution: A pendulum consists of a bob of mass m = 0.1 kg and a massless…

A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse P = 0.2 kg-m/s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is J kg-m2/s. The kinetic energy of the pendulum just after the lift-off is K Joules.

The value of K is ___________.

Step-by-Step Verified Solution

Angular momentum, L = P ×\times 0.9 = 0.18 kgm2/s

JEE Advanced 2021 Paper 2 Online Physics - Impulse & Momentum Question 10 English Explanation
Just after string becomes taut; there will be no velocity along the string.

∴\therefore V⊥=Pcos⁡θm=0.2×0.91×0.1=1.8{V_ \bot } = {{P\cos \theta } \over m} = {{0.2 \times 0.9} \over {1 \times 0.1}} = 1.8 m/s

∴\therefore K=12mv⊥2=12×0.1×1.82=0.162K = {1 \over 2}mv_ \bot ^2 = {1 \over 2} \times 0.1 \times {1.8^2} = 0.162 J

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