Question

A heavy stone hanging from a massless string of length 15 m is projected horizontally with a speed of 147 m/s speed in which tension is equal to weight

Answer 1

A heavy stone hanging from a massless string of length 15m is projected horizontally with a speed of 147 m/s.

To find : the speed of stone in which tension is equal to weight.

solution : a/c to question, we have to find the speed of stone, v in which tension, T is equal to weight, mg.

i.e., T = mg ......(1)

let stone makes an angle θ with the vertical.

so, height of stone from the ground, h = l(1 - cosθ)

using law of conservation of energy,

1/2 m(v² - u²) = -mgh

⇒v² - u² = -2gh

⇒v² = u² - 2gh

⇒v² = u² - 2gl(1 - cosθ) .........(2)

at equilibrium,

T - mgcosθ = mv²/l

⇒mg - mgcosθ = m[u² - 2gl(1 - cosθ)]/l

⇒gl(1 - cosθ) = u² - 2gl(1 - cosθ)

⇒3gl(1 - cosθ) = u²

now putting value of u = 147 m/s, l = 15 m and g = 10m/s²

⇒3 × 10 × 15(1 - cosθ) = 147

⇒1 - cosθ = 147/450

⇒cosθ = 303/450

now v² = u² - 2gl(1 - 303/450) [ from equation (2) ]

⇒v² = u² - 147gl/225

⇒v² = 147 - 147gl/225 = 147[225 - 10 × 15]/225

⇒v² = 147 × 75/225 = 147/3 = 49

⇒v = 7 m/s

Therefore the speed of stone in which tension is equal to weight.