Question

A light string passing over a smooth light pulley connects two block of masses m₁ and m₂ (vertically). If the acceleration of the system is (3g/7), then the ratio of masses is ____________.

Options

• 8 : 1

• 9 : 7

• 1.4 : 3

• 2.25 : 1

Answer 1

A light string passing over a smooth light pulley connects two block of masses m₁ and m₂ (vertically). If the acceleration of the system is (3g/7), then the ratio of masses is 2.25 : 1.

Explanation:

When two masses m₁ and m₂ are connected to the two ends of an inextensible string passing over a smooth frictionless pulley, then the acceleration of the masses is given by:

`"a"= (("m"_1 - "m"_2)/("m"_1 + "m"_2))"g"`

Here a= 3g/7

`therefore (3"g")/7 = (("m"_1 - "m"_2)/("m"_1 + "m"_2))"g"`

3m₁ + 3m₂ = 7m₁ - 7m₂

4m₁ = 10 m₂

`"m"_1/"m"_2 = 10/4`

`therefore "m"_1/"m"_2 = 2.25`