The answer to number 1 is D and the answer for the second one is 2
^-^
Answer:
option C
Explanation:
the ball is moving circular around the pole
Angular momentum of the system is constant
J = I ω
now,



the rope radius is decreasing as it revolving around the pole
angular speed is inversely proportional to radius.
so, the angular speed will increase.
The correct answer is option C
by the formula of spring force we know that

here we know that


now we will have


now by similar way if the stretch in spring is 0.25 m
force is given by



so it will require F = 250 N force
M = 2.2 g = 2.2 x 10⁻³ kg, the mass of the bug.
r = 3.0 cm = 0.03 m, the radial distance from the center.
The angular speed is
ω = 280 rpm
= (280 rev/min)*(2π rad/rev)*(1/60 min/s)
= 29.3215 rad/s
The moment of inertia of the bug is
I = mr²
= (2.2 x 10⁻³ kg)*(0.03 m)²
= 1.98 x 10⁻⁶ kg-m²
Calculate the angular momentum of the bug.
J = Iω
= (1.98 x 10⁻⁶ kg-m²)*(29.3215 rad/s)
= 5.806 x 10⁻⁵ (kg-m²)/s
Answer: 5.806 x 10⁻⁵ (kg-m²)/s