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QJEEM21Ph2b13: JEE Main 2021 Physics - Class 11 JEEM21Ph2b13 Solution: In the reported figure, two bodies A and B of masses 200 g and…

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.

JEE Main 2021 (Online) 25th July Morning Shift Physics - Simple Harmonic Motion Question 75 English

Step-by-Step Verified Solution

ω=keqμ\omega = \sqrt {{{{k_{eq}}} \over \mu }}

μ\mu = reduced mass

springs are in series connection

keq=k1k2k1+k2{k_{eq}} = {{{k_1}{k_2}} \over {{k_1} + {k_2}}}

keq=k×4k5k=4k5{k_{eq}} = {{k \times 4k} \over {5k}} = {{4k} \over 5}

keq=4×205{k_{eq}} = {{4 \times 20} \over 5} N/m = 16 N/m

μ=m1m2m1+m2=0.2×0.80.2+0.8=0.16\mu = {{{m_1}{m_2}} \over {{m_1} + {m_2}}} = {{0.2 \times 0.8} \over {0.2 + 0.8}} = 0.16 kg

ω=160.16=100=10\omega = \sqrt {{{16} \over {0.16}}} = \sqrt {100} = 10

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