Question

A stone of mass m tied to the end of a string revolves in a vertical circle of radius R. The net forces at the lowest and the highest points of the circle directed vertically downwards are:
Lowest point
a. mg - T₁
b. mg + T₁
c. $mg + T_1- \frac{(mv_1^2)}{R}$
d. $mg - T_1- \frac{(mv_1^2)}{R}$

Highest point
mg + T₂
mg - T₂
$mg - T_2- \frac{(mv_1^2)}{R}$
$mg + T_2- \frac{(mv_1^2)}{R}$

T₁ and v₁ denote the tension and speed at the lowest point. T₂ and v₂ denote the corresponding values at the highest point.

Answer 1

Hey mate,

# Answer-
a) At lowest point F = T1 - mg
b) At highest point F = T2 + mg

## Explaination-
a) At lowest point,
Centripetal force = mv1^2/r
By Newton's 2nd law of motion,
T1 - mg = mv1^2/r
Here, net force is nothing but centripetal force.
F = mv1^2/r = T1 - mg

a) At highest point,
Centripetal force = mv2^2/r
By Newton's 2nd law of motion,
T2 + mg = mv2^2/r
Here, net force is nothing but centripetal force.
F = mv2^2/r = T1 + mg

Hope that solved your query...