Question

Two weights w₁ and w₂ are suspended from the ends of light string over a smooth fixed pulley. If the pulley is pulled up with acceleration g, the tension in the string will be ______.

पर्याय

• `(4"w"_1"w"_2)/("w"_1+"w"_2)`

• `(2"w"_1"w"_2)/("w"_1+"w"_2)`

• `("w"_1-"w"_2)/("w"_1+"w"_2)`

• `("w"_1"w"_2)/(2("w"_1+"w"_2))`

Answer 1

Two weights w₁ and w₂ are suspended from the ends of light string over a smooth fixed pulley. If the pulley is pulled up with acceleration g, the tension in the string will be `bbunderline((4"w"_1"w"_2)/("w"_1+"w"_2))`.

Explanation:

For solving the problem, we assume that observer is situated in the fram of pulley (non inertial reference frame).

m₁g = w₁

m₂g = w₂

From force diagram,

T - m₂a₀ - w₂ = m₂a

or T - m₂g - w₂ = m₂a       (∴ a₀ = g)

or T - 2w₂ = m₂a         ...(i)

from force diagram

or m₁g + w₁ - T = ma₁a      (∴ a₀ = g)

or 2w₁ - T = m₁a         ...(ii)

From eqs. (i) and (ii), we get

T = `(4"w"_1"w"_2)/("w"_1+"w"_2)`