A simple pendulum is hanging from a peg inserted in a vertical wall. Its bob is stretched in horizontal position from the wall and is

Q: A simple pendulum is hanging from a peg inserted in a vertical wall. Its bob is stretched in horizontal position from the wall and is left free to move. The bob hits on the wall the coefficient of restitution is $\frac{2}{{\sqrt 5 }}$. After how many collisions the amplitude of vibration will become less than $60°$

b (b) From the relation of restitution $\frac{{{h_n}}}{{{h_0}}} = {e^{2n}}$ and ${h_n} = {h_0}(1 - \cos 60^\circ )$ $⇒$ $\frac{{{h_n}}}{{{h_0}}} = 1 - \cos 60^\circ = {\left( {\frac{2}{{\sqrt 5 }}} \right)^{2n}}$ $⇒$ $1 - \frac{1}{2} = {\left( {\frac{4}{5}} \right)^n}$ $⇒$ $\frac{1}{2} = {\left( {\frac{4}{5}} \right)^n}$ Taking log of both sides we get $\log 1 - \log 2 = n(\log 4 - \log 5)$ $0 - 0.3010 = n(0.6020 - 0.6990)$ $ - \,0.3010 = - n \times 0.097$ ==> $n = \frac{{0.3010}}{{0.097}} = 3.1 \approx 3$

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

A simple pendulum is hanging from a peg inserted in a vertical wall. Its bob is stretched in horizontal position from the wall and is left free to move. The bob hits on the wall the coefficient of restitution is $\frac{2}{{\sqrt 5 }}$. After how many collisions the amplitude of vibration will become less than $60°$

A$6$
B$3$
C$5$
D$4$

Diffcult

STD 11 Science
NEET
STD 11 - 13. oscillations
Physics

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