JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Elasticity & SHM

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In the reported figure, two bodies A and B of masses 200 g and 800 g are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be ____

rad / s

when

k = 20 N / m

Answer: 10

Solution

The two springs lie one after the other between the blocks, so the pair behaves as a single spring of constant

k_{eff} = \frac{k ( 4 k )}{k + 4 k} = \frac{4 k}{5} = 16 N/m

The surface is frictionless and no external horizontal force acts, so the centre of mass stays put and the two blocks oscillate about it. The inertia that enters the oscillation is the reduced mass

μ = \frac{m _{A} m _{B}}{m _{A} + m _{B}} = \frac{0.2 \times 0.8}{1.0} = 0.16 kg

so the angular frequency is

ω = \frac{k _{eff}}{μ} = \frac{16}{0.16} = 10

rad/s.

JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Numerical answer

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JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Elasticity & SHM

Solution

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