13.Oscillations
medium

$0.5\, m$ લંબાઇના સાદા લોલકને સમતોલન સ્થાન પાસે $3\, m/s$ નો વેગ આપતાં $ {60^o} $ ના ખૂણે તેનો વેગ કેટલો .... $m/s$ થાય? ( $ g = 10\,m/{s^2} $ )

A

$3$

B

$0.33$

C

$0.5$

D

$2$

Solution

(d) Let bob velocity be $v$ at point $B$ where it makes an angle of $60^o$ with the vertical, then using conservation of mechanical energy

$K{E_A} + P{E_A} = K{E_B} + P{E_B}$

==> $\frac{1}{2}m \times {3^2} = \frac{1}{2}m{v^2} + mgl(1 – \cos \theta )$

$⇒ 9 = {v^2} + 2 \times 10 \times 0.5 \times \frac{1}{2} $

$⇒ v = 2\,m/s$

Standard 11
Physics

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