Question

The bob of a pendulum was released from a horizontal position. The length of the pendulum is 10m. If it dissipates 10% of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is : [Use, g : 10 \(ms^{–2}\) ]

(1) \(6\sqrt5\, ms^{-1}\)

(2) \(5\sqrt6\, ms^{-1}\)

(3) \(5\sqrt5\, ms^{-1}\)

(4) \(2\sqrt5\, ms^{-1}\)

Answer 1

The correct option is (1) \(6\sqrt5\, ms^{-1}\)

\(E_A - loss = E_B\)

\(mgl - 0.1mgl = \frac{1}{2} mv^2\)

\(\Rightarrow v = \sqrt{0.9 \times 2 \times 10 \times 10}\, m/s\)

\(\Rightarrow v = 6\sqrt5\, ms^{-1}\)