Gravitation

Statement 1 is correct.

Let m1, m2 be the masses of P and Q respectively, and r1 and r2 be their respective distances from O.
Thus, r1 = 2(r2)

Taking moment about O,
(m1).(r1) = (m2).(r2)
(m1).(2.r2) = (m2).(r2)
i.e. 2(m1) = m2
or m1 = (m2)/2

Statement 2 is wrong

Gravitational attraction between P and Q
= G(m1)(m2)/(r1+r2)^2 where G is the Universal Gravitational Constant
= G(m1).(2.m1)/(r1+r1/2)^2
= 2G(m1)^2/(9.(r1)^2/4)
= 8G(m1)^2/[9.(r1)^2]

Required centripetal force on P
= (m1)(v1)^2/r1 where v1 is the speed of P
Hence, 8G(m1)^2/[9.(r1)^2] = (m1)(v1)^2/r1
v1^2 = 8G(m1)/9(r1)

For star Q: 8G(m1)^2/[9.(r1)^2] =(m2).(v2)^2/(r2)
(v2)^2 = 2G(m1)/[9(r1)]

Hence, (v1/v2)^2 = 4
v1/v2 = 2

Statement 3 is correct.

Acceleration of P = (v1)^2/r1
Acceleration of Q = (v2)^2/r2 = (v1/2)^2/(r1/2) = (1/2).(v1)^2/r1
Hence, acceleration of P to that of Q = [(v1)^2/(r1)]/[(v1)^2/(2.r1)] = 2