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).

Options

A. Time period of the pendulum is `2pi sqrt((l)/(g))`.
B. The equation of motion for this pendulum is `theta = (v_(0))/(2sqrt(gl))sin [sqrt((g)/(l)t)]`
C. The equation of motion for this pendulum is `theta = (v_(0))/(2sqrt(g))cos[sqrt((g)/(l)t)]`
D. Time period of the pendulum is `2pi sqrt((2l)/(g))`

Answer

A, B

Explanation

`T = 2pi sqrt((l)/(g))`, independent of mass of bob:
Equation of motion is: `theta = theta_(0) sin omegat`
Calculation of `theta_(0)` is from law of conservation of energy.`(1)/(2) (2m) ((v_(0))/(2))^(2) = 2mgl (1-cos theta_(0)) rArr theta_(0) = ?`