Two bodies A, B of masses $m_1, m_2$ are knotted to a mass-less string at different points rotated along concentric circles in horizontal plane. The distances of A, B from common centre are 50cm, 1m. If the tensions in the string between centre to A and A to B are in the ratio 5:4, then the ratio of $m_{1}$ to $m_{2}$ is:

A stone of mass $0.2kg$ is tied to one end of a thread of length $0.1m$ whirled in a vertical circle. When the stone is at the lowest point of circle, tension in thread is $52N$, then velocity of the stone will be:

An aeroplane flying in the sky with a uniform speed of 200 m/s moves in a vertical circle of radius 400 m. The mass of the pilot is 70 kg. The force exerted by the pilot on the seat at the lowest point on the circle will be(g=10 m/s^2)

A particle of mass m attached with a string of length $l$ is just revolving on the vertical circle without slacking of the string. If $v_A, v_B$ and $v_D$ are speeds at positions A, B and D, then

A toy car is tied to the end of an unstretched string of a length, $a$. When revolved, the toy car moves in a horizontal circle of radius $2a$ with time period, $T$. If it is now revolved in a horizontal circle of radius $3a$ with a period $T'$ with the same force, then