The velocity of a particle executing SHM varies with displacement ( x) as 4v² = 50 - x². The time period of oscillations is x/7 s. The value of x is (Take π = 22/7) (a) 82 (b) 84 (c) 88 (d) 90

Answer: (c). Compare v² = 1/4(50 - x²) with v² = ω²(A² - x²): ω² = 1/4, ω = 1/2 rad/s. T = (2π)/(ω) = 4π = 4×22/7 = 88/7 s. x/7 = 88/7 ⇒ x = 88. So the answer is (c) 88.

The velocity of a particle executing SHM varies with displacement (… | MHT CET 2026 (13 Apr, Shift 2)

Q11MHT CET 2026 · 13 APR · SHIFT 2Medium

Velocity & Acceleration in SHM

The velocity of a particle executing SHM varies with displacement ( $x$ ) as $4v^2 = 50 - x^2$ . The time period of oscillations is $x/7$ s.

The value of $x$ is (Take $\pi = 22/7$ )

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Answer: (c)

Compare $v^2 = \frac{1}{4}(50 - x^2)$ with $v^2 = \omega^2(A^2 - x^2)$ : $\omega^2 = \frac{1}{4}$ , $\omega = \frac{1}{2}$ rad/s.
$T = \frac{2\pi}{\omega} = 4\pi = 4\times\frac{22}{7} = \frac{88}{7}$ s.
$\frac{x}{7} = \frac{88}{7} \Rightarrow x = 88$ .
So the answer is (c) 88.

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Velocity & Acceleration in SHM question from MHT CET 2026 (13 Apr, Shift 2)

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