A ball of mass 'm' is suspended from a point with a massless string of length `l` in form of a pendulum. This ball is given a horizontal velocity `sqrt(4 gl)` at bottom most point. When string makes an angle `60^(@)` from lower vertical, `(a_(c))/(a_(t))=p`. write the value of `p^(2)`. `(g=10 m//s^(2))`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Analyze the System
We have a pendulum with a mass \( m \) suspended from a point with a massless string of length \( l \). The ball is given an initial horizontal velocity of \( v_0 = \sqrt{4gl} \) at the lowest point.

### Step 2: Determine the Velocity at \( 60^\circ \)
When the pendulum makes an angle of \( 60^\circ \) with the vertical, we need to find the velocity of the ball at this position. We can use the conservation of mechanical energy.

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