Physics And Measurement Question 30

Question: A highly rigid cubical block $ A $ of small mass $ M $ and side $ L $ is fixed rigidly onto another cubical block $ B $ of the same dimensions and of low modulus of rigidity $ \eta $ such that the lower face of $ A $ completely covers the upper face of $ B $ . The lower face of $ B $ is rigidly held on a horizontal surface. A small force $ F $ is applied perpendicular to one of the side faces of $ A $ . After the force is withdrawn block $ A $ executes small oscillations. The time period of which is given by

[IIT 1992]

Options:

A) $ 2\pi \sqrt{\frac{M\eta }{L}} $

B) $ 2\pi \sqrt{\frac{L}{M\eta }} $

C) $ 2\pi \sqrt{\frac{ML}{\eta }} $

D) $ 2\pi \sqrt{\frac{M}{\eta L}} $

Show Answer

Answer:

Correct Answer: D

Solution:

By substituting the dimensions of mass [M], length [L] and coefficient of rigidity $ [ M{{L}^{-1}}{{T}^{-2}} ] $ we get $ T=2\pi \sqrt{\frac{M}{\eta L}} $ is the right formula for time period of oscillations



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