The velocity of particle executing S.H.M. varies with displacement (x) as 4V² = 50 - x². The time period of oscillation is x/7 second. The value of ' x ' is (Take π = 22/7) (a) 22 (b) 44 (c) 66 (d) 88

Answer: (d). v² = 1/4(50 - x²) compared with v² = ω²(A² - x²) gives ω = 1/2 rad/s. T = (2π)/(ω) = 4π = 88/7 s. x/7 = 88/7 ⇒ x = 88. So the answer is (d) 88.

The velocity of particle executing S.H.M. varies with displacement… | MHT CET 2024 (4 May, Shift 1)

Q28MHT CET 2024 · 4 MAY · SHIFT 1Medium

Velocity & Acceleration in SHM

The velocity of particle executing S.H.M. varies with displacement $(x)$ as $4V^2 = 50 - x^2$ . The time period of oscillation is $\frac{x}{7}$ second. The value of ' $x$ ' is (Take $\pi = \frac{22}{7}$ )

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Answer: (d)

$v^2 = \frac{1}{4}(50 - x^2)$ compared with $v^2 = \omega^2(A^2 - x^2)$ gives $\omega = \frac{1}{2}$ rad/s.
$T = \frac{2\pi}{\omega} = 4\pi = \frac{88}{7}$ s.
$\frac{x}{7} = \frac{88}{7} \Rightarrow x = 88$ .
So the answer is (d) 88.

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Velocity & Acceleration in SHM question from MHT CET 2024 (4 May, Shift 1)

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