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A pendulum bob has a speed of $3\, {m} / {s}$ at its lowest position. The pendulum is $50 \,{cm}$ long. The speed of bob, when the length makes an angle of $60^{\circ}$ to the vertical will be $ .......\,{m} / {s}$ $\left(g=10 \,{m} / {s}^{2}\right)$
A man having a wrist watch and a pendulum clock rises on a $TV$ tower. The wrist watch and pendulum clock per chance fall from the top of the tower. Then
A particle of mass $10\, gm$ moves in a field where potential energy per unit mas is given by expression $v = 8 \times 10^4\, x^2\, erg/gm$. If the total energy of the particle is $8 \times 10^7\, erg$ then the relation between $x$ and time $t$ is
A pendulum is suspended by a string of length $250\,cm$. The mass of the bob of the pendulum is $200\,g$. The bob is pulled aside until the string is at $60^{\circ}$ with vertical as shown in the figure. After releasing the bob. the maximum velocity attained by the bob will be________ $ms ^{-1}$. (if $g=10\,m / s ^{2}$ )
A tunnel is dug in the earth across one of its diameter. Two masses $‘m’\,\& \,‘2m’$ are dropped from the ends of the tunnel. The masses collide and stick to each other and perform $S.H.M.$ Then amplitude of $S.H.M.$ will be : [$R =$ radius of the earth]
A body of mass $0.01 kg$ executes simple harmonic motion $(S.H.M.)$ about $x = 0$ under the influence of a force shown below : The period of the $S.H.M.$ is .... $s$