Question

A mass m is revolving in a vertical circle at the end of a string of length 20 cm. By how much does the tension of the string at the lowest point exceed the tension at the topmost point?

Options

• 2 mg

• 4 mg

• 6 mg

• 8 mg

Answer 1

6 mg

Explanation:

The tension T₁ at the topmost point is given by 

T₁ = `("mv"_1^2)/20-"mg"`

weight acting downward and centrifugal force acting outward.

The tension T₂ at the lowest point

T₂ = `"mv"_2^2/20+"mg"`

Centrifugal force and weight (both) acting downward

T₂ - T₁ = `("mv"_2^2-"mv"_1^2)/20+2` mg

`"v"_1^2="v"_2^2-2  "gh" or "v"_2^2-"v"_1^2`

= 2g (40) = 80 g

∴ T₂ - T₁ = `(80"mg")/20+2 "mg"`

= 6 mg