Answer:
Explanation:
Given
mass of sphere 
diameter of sphere 
radius 

friction will provide resisting torque so
where 







(b)time taken to decrease its rotational speed by 



Answer:
The ratio of lengths of the two mathematical pendulums is 9:4.
Explanation:
It is given that,
The ratio of periods of two pendulums is 1.5
Let the lengths be L₁ and L₂.
The time period of a simple pendulum is given by :

or

Where
l is length of the pendulum

or
....(1)
ATQ,

Put in equation (1)

So, the ratio of lengths of the two mathematical pendulums is 9:4.
Answer:
K_{total} = 19.4 J
Explanation:
The total kinetic energy that is formed by the linear part and the rotational part is requested

let's look for each energy
linear
= ½ m v²
rotation
= ½ I w²
the moment of inertia of a solid sphere is
I = 2/5 m r²
we substitute
= ½ mv² + ½ I w²
angular and linear velocity are related
v = w r
we substitute
K_{total} = ½ m w² r² + ½ (2/5 m r²) w²
K_{total} = m w² r² (½ + 1/5)
K_{total} =
m w² r²
let's calculate
K_{total} =
6.40 16.0² 0.130²
K_{total} = 19.4 J
if one of the charge is doubled, the electric potential energy would be doubled too