JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Work, Power & Energy

The bob of a pendulum was released from a horizontal position. The length of the pendulum is 10 m. 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

^{- 2}

]

Answer: (A)

Solution

Taking the lowest point of the swing as the reference level, the bob falls through a height equal to the pendulum length

ℓ = 10

m as it swings from the horizontal to the bottom. The full mechanical energy available for this fall is

m g ℓ

.

Since 10% of this energy is dissipated by air resistance, only 90% converts to kinetic energy at the lowest point:

\frac{1}{2} m v^{2} = 0.9 m g ℓ

v^{2} = 1.8 g ℓ = 1.8 \times 10 \times 10 = 180

v = 180 = 65 m/s

JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Single correct option