Principal of Conservation of Energy: Practice Problem & Solution

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Principal of Conservation of Energy. Understanding the underlying formula is key to arriving at the correct answer below:

Let the initial height be \(S\). At height \(h\), \(KE = 3PE = 3mgh\). By conservation of energy, \(mgS = mgh + 3mgh = 4mgh\), so \(h = S/4\). Also, \(KE = \frac{1}{2}mv^2 = 3mgh\), substituting \(h\) gives \(v^2 = 6g(S/4) = \frac{3gS}{2}\), so \(v = \sqrt{\frac{3gS}{2}}\).