JEE Main · 2023 · 06 Apr 2023 · Shift 2 · Elasticity & SHM

A simple pendulum with length 100 cm and bob of mass 250 g is executing S.H.M. of amplitude 10 cm. The maximum tension in the string is found to be

\frac{x}{40}

N. The value of x is ____.

Answer: 99

Solution

With amplitude

A = 10

cm and length

l = 100

cm, the angular amplitude satisfies

sin θ_{0} = \frac{A}{l} = \frac{1}{10}

. The speed at the lowest point follows from energy conservation,

\frac{1}{2} m v^{2} = m g l (1 - cos θ_{0})

, so

v^{2} = 2 g l (1 - cos θ_{0})

. At the lowest point the radial equation is

T - m g = \frac{m v ^{2}}{l}

, giving

T = m g [3 - 2 cos θ_{0}]

with

cos θ_{0} = 1 - sin^{2} θ_{0} = 1 - \frac{1}{100}

. Taking

m = 0.25

kg and

g = 9.8

m s

^{- 2}

T = 0.25 \times 9.8 \times [3 - 2 (1 - \frac{1}{200})] = 2.45 \times 1.01 = \frac{99}{40}

N. The value of

x

99

JEE Main · 2023 · 06 Apr 2023 · Shift 2 · Integer answer