Laws of Motion · Question 17

A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be : (g = 10 m/s2)

1. 102 rad/s
2. 10 rad/s
3. 10 rad/s
4. 10 rad/s

A particle moving with velocity V is acted by three forces shown by the vector triangle PQR. The velocity of the particle will : [figure]

1. remain constant
2. increase
3. decrease
4. change according to the smallest force QR

Which one of the following statements is incorrect?

1. Rolling friction is smaller than sliding friction.
2. Limiting value of static friction is directly proportional to normal reaction.
3. Frictional force opposes the relative motion.
4. Coefficient of sliding friction has dimensions of length.

A block of mass m is placed on a smooth inclined wedge ABC of inclination as shown in the figure. The wedge is given an acceleration 'a' towards the right. The relation between a and for the block to remain stationary on the wedge is [figure]

1. a = gcosec
2. a = g
3. a = g
4. a = g

One end of string of length l is connected to a particle of mass 'm' and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed 'v', the net force on the particle (directed towards centre) will be (T represents the tension in the string)

1. T + mv2l
2. T - mv2l
3. zero
4. T

Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively [figure]

1. g3, g
2. g, g
3. g3, g3
4. g, g3

A car is negotiating a curved road of radius R. The road is banked at an angle . The coefficient of friction between the tyres of the car and the road is s. The maximum safe velocity on this road is

1. gR s + 1 - s
2. gR2 s + 1 - s
3. gR2 s + 1 - s
4. gR s + 1 - s

A rigid ball of mass m strikes a rigid wall at 60 and gets reflected without loss of speed as shown in the figure. The value of impulse imparted by the wall on the ball will be : [figure]

1. mV
2. 2 mV
3. mV2
4. mV3

A bullet of mass 10 g moving horizontally with a velocity of 400 m s-1 strikes a wood block of mass 2 kg which is suspended by light inextensible string of length 5 m. As a result, the centre of gravity of the block is found to rise a vertical distance of 10 cm. The speed of the bullet after it emerges out horizontally from the block will be

1. 100 m s-1
2. 80 m s-1
3. 120 m s-1
4. 160 m s-1

Two stones of masses m and 2m are whirled in horizontal circles, the heavier one in a radius r2 and the lighter one in radius r. The tangential speed of lighter stone is n times that of the value of heavier stone when they experience same centripetal forces. The value of n is

1. 4
2. 1
3. 2
4. 3