Question

Two identical masses are connected to a horizontal thin (massless) rod as shown in the figure. When their distance from the pivot is D, a torque τ produces an angular acceleration of α₁. The masses are now repositioned so that they are 2D from the pivot. The same torque produces an angular acceleration α₂ which is given by ______

  

Options

• α₂ = 4α₁

• α₂ = α₁

• α₂ = `1/2alpha_1`

• α₂ = `1/4alpha_1`

Answer 1

Two identical masses are connected to a horizontal thin (massless) rod as shown in the figure. When their distance from the pivot is D, a torque τ produces an angular acceleration of α₁. The masses are now repositioned so that they are 2D from the pivot. The same torque produces an angular acceleration α₂ which is given by `underline(alpha_2 = 1/4alpha_1)`.

Explanation:

Torque producing acceleration α₁

∴ `tau = "I"_1alpha_1 = 2"m""D"^2alpha_1`

Same torque produces α₂

∴ `tau = "I"_2alpha_2 = 2"m"(2"D")^2alpha_2`

∴ `4(2"mD"^2)alpha_2 = 2"mD"^2alpha_1`

∴ `alpha_2 = 1/4alpha_1`.