Answer:
w = vR/3
Explanation:
The centre of mass of the loop to bullet system is given by D / 4 from centre of loop, which is equivalent to R / 2 from its centre.
From the principle of conservation of linear momentum
, we have
m*v = 2*m* Vcm
Where v = velocity of bullet, Vcm = velocity of wood
Hence, we have
Vcm = v2
Also, from the conservation of angular momentum about the centre of mass.
M*V*(R/2) = Ic*w - equation (I)
where Ic = moment of inertia and w = angular velocity
Ic for a ring is given by
Ic of a bullet is given by
Hence, the moment of inertia of the system is given by the summation of the two moments of inertia Ic(ring) + Ic(bullet) which gives
Ic(system) = 
Substituting back into equation (I), we have

Hence, we obtain w =vR/3
w=v3R
Answer:

Explanation:
As we know that the displacement of the particle from the mean position is 1/5 times of its amplitude
so we have


so now we have

now we have

so the phase other particle in opposite direction is given as

so we have phase difference given as


Answer:
0.5mv^2=50, v=5, 25/2×m=50, m=50×2/25, So, the answer is 4