A bob of mass `M` is hung using a string of length `l`. A mass `m` moving with a velocity `u` pierces thorugh the bob and emerges out with velocity `(u)/(3)` horizontally. The frequency of small oscillations of the bib, considering `A` as amplitude is,

A bullet of mass m strikes a pendulum bob of mass 2m with velocity u es shown in figure. If passes through and emerges but with a velocity u//2 from bob. The length of the pendulum bob is l = 2m . If the minimum value of u for which the pendulum bob completes full circle is 10X m//s , then find X . (Take g = 10 m//s^(2) )

A bullet of mass m strikes a pendulum bob of mass 2m with velocity u es shown in figure. If passes through and emerges but with a velocity u//2 from bob. The length of the pendulum bob is l = 2m . If the minimum value of u for which the pendulum bob completes full circle is 10X m//s , then find X . (Take g = 10 m//s^(2) )

A simple pendulum consists of a bob of mass m and a light string of length l as shown in the fig. another identical ball moving with the small velocity v_0 collides with the pendulum's bob and sticks to it. For this new pendulum of mass 2 m, mark out the correct statements (s).

A simple pendulum consists of a bob of mass m and a light string of length l as shown in the fig. another identical ball moving with the small velocity v_0 collides with the pendulum's bob and sticks to it. For this new pendulum of mass 2 m, mark out the correct statements (s).

A bob of mass M is suspended by a massless string of length L. The horizontal velocity v at position A is just sufficient to make it reach the point B. The angle theta at which the speed of the bob is half of that at A, satisfies

A bob of mass m, suspended by a string of length l_1 is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length l_2 , which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio (l_1)/(l_2) is