Two masses, \(M\) and \(m\), are attached to a vertical axis by weightless threads of combined length \(l\). They are set in rotational motion in a horizontal plane about this axis with constant angular velocity \(\omega\). If the tensions in the threads are the same during motion, the distance of \(M\) from the axis is:
1. \(\frac{M l}{M + m}\)
2. \(\frac{m l}{M + m}\)
3. \(\frac{M+m}{M}l\)
4. \(\frac{M+m}{m}l\)

A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved 

(1) 14 m/s

(2) 3 m/s

(3) 3.92 m/s

(4) 5 m/s

A point mass m is suspended from a light thread of length l, fixed at O, is whirled in a horizontal circle at constant speed as shown. From your point of view, stationary with respect to the mass, the forces on the mass are

(1)
(2)
(3)
(4)

A motor cycle driver doubles its velocity when he is having a turn. The force exerted outwardly will be

(1) Double

(2) Half

(3) 4 times

(4) $\frac{1}{4}$ times

A mass is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity ω₀. If the length of the string and angular velocity are doubled, the tension in the string which was initially T₀ is now 

(1) T₀

(2) T₀/2

(3) 4 T₀

(4) 8 T₀

An object with a mass 10 kg moves at a constant velocity of 10 m/sec. A constant force then acts for 4 second on the object and gives it a speed of 2 m/sec in opposite direction. The acceleration produced in it, is 

(1) 3 m/sec²

(2) –3 m/sec²

(3) 0.3 m/sec²

(4) –0.3 m/sec²

A machine gun is mounted on a 2000 kg car on a horizontal frictionless surface. At some instant the gun fires bullets of mass 10 gm with a velocity of 500 m/sec with respect to the car. The number of bullets fired per second is ten. The average thrust on the system is 

(1) 550 N

(2) 50 N

(3) 250 N

(4) 250 dyne

A cricket ball of mass 250 g collides with a bat with velocity 10 m/s and returns with the same velocity within 0.01 second. The force acted on bat is 

(1) 25 N

(2) 50 N

(3) 250 N

(4) 500 N

If rope of lift breaks suddenly, the tension exerted by the surface of lift (a = acceleration of lift) 

(1) mg

(2) m(g + a)

(3) m(g – a)

(4) 0

A plumb line is suspended from a ceiling of a car moving with horizontal acceleration of a. What will be the angle of inclination with vertical 

(1) tan^–1(a/g)

(2) tan^–1(g/a)

(3) cos^–1(a/g)

(4) cos^–1(g/a)