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. Coefficient of sliding friction has dimensions of length.
4. Frictional force opposes the relative motion.
A block of mass m is placed on a smooth inclined wedge ABC of inclination θ as shown in the figure. The wedge is given an acceleration a towards the right. The relation between a and θ for the block to remain stationary on the wedge is
1.
2.
3.
4.
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 center) will be (T represents the tension in the string)
1. T
2.
3.
4. Zero
Suppose the charge of a proton and an electron differ slightly. One of them is –e, the other is (e + Δe). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then Δe is of the order of [Given mass of hydrogen mh = 1.67 × 10–27 kg]
1. 10–20 C
2. 10–23 C
3. 10–37 C
4. 10–47 C
A rigid ball of mass m strikes a rigid wall at 60° and gets reflected without loss of speed as shown in the figure below. The value of impulse imparted by the wall on the ball will be
1. mV
2. 2mV
3.
4.
A car is negotiating a curved road of radius R. The road is banked at an angle θ. The coefficient of friction between the tyres of the car and the road is μs. The maximum safe velocity on this road is
1.
2.
3.
4.
A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30º, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank will be, respectively
1. 0.4 and 0.3
2. 0.6 and 0.6
3. 0.6 and 0.5
4. 0.5 and 0.6
Two stones of masses m and 2 m are whirled in horizontal circles, the heavier one in a radius and 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. 1
2. 2
3. 3
4. 4
Three blocks A, B and C of masses 4 kg, 2 kg and 1 kg respectively, are in contact on a frictionless surface, as shown. If a force of 14 N is applied on the 4 kg block, then the contact force between A and B is
1. 18 N
2. 2 N
3. 6 N
4. 8 N
A block A of mass m1 rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of table and from its other end another block B of mass m2 is suspended. The coefficient of kinetic friction between the block and table is μk. When the block A is sliding on the table, the tension in the string is
1.
2.
3.
4.
A system consists of three masses m1, m2 and m3 connected by a string passig over a pulley P. The mass m1 hangs freely and m2 and m3 are on a rough horizontal table (The coefficient of friction = μ). The pulley is frictionless and of negligible mass. The downward acceleration of mass m1 is: (Assume m1 = m2 = m3 = m)
1.
2.
3.
4.
The force F acting on a particle of mass m is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from 0 s to 8 s is
1. 24 Ns
2. 20 Ns
3. 12 Ns
4. 6 Ns
A balloon with m is descending down with an acceleration a (where a < g). How much mass should be removed from it so that it starts moving up with an acceleration a?
1.
2.
3.
4.
The upper half of an inclined plane of inclination θ is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by
1.
2.
3.
4.
Three blocks with masses m, 2m and 3m are connected by strings, as shown in the figure. After an upward force F is applied on block m, the masses move upward at constant speed v. What is the net force on the block of mass 2m? (g is the acceleration due to gravity)
1. 2mg
2. 3mg
3. 6mg
4. Zero
An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. the first part of mass 1 kg moves with a speed of 12 ms–1 and the second part of mass 2 kg moves with 8 ms–1 speed. If the third part flies off with 4 ms–1 speed, then its mass is
1. 5 kg
2. 7 kg
3. 17 kg
4. 3 kg
A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45°, the speed of the car is
1. 5 ms–1
2. 10 ms–1
3. 20 ms–1
4. 30 ms–1
A car of mass m is moving on a level circular track of radius R. If μs represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by
1.
2.
3.
4.
A person of mass 60 kg is inside a lift of mass 940 kg and presses the button on control panel. The lift starts moving upwards with an acceleration 1 m/s2. If g = 10 ms–2, the tension in the supporting cable is
1. 1200 N
2. 8600 N
3. 9680 N
4. 11000 N
A body of mass M hits normally a rigid wall with velocity v and bounces back with the same velocity. The impulse experienced by the body is
1. Zero
2. Mv
3. 1.5Mv
4. 2Mv
A radioactive nucleus of mass M emits a photon of frequency ν and the nucleus recoils. The recoil energy will be:
1. hν
2. Mc2 – hν
3.
4. Zero
A block of mass m is in contact with the cart C as shown in the figure.
The coefficient of static friction between the block and the cart is μ. The acceleration of the cart that will prevent the block from falling satisfies :
1.
2.
3.
4.
A gramophone record is revolving with an angular velocity ω. A coin is placed at a distance r from the centre of the record. The static coefficient of friction is μ. The coin will revolve with the record if:
1.
2.
3.
4.
A body, under the action of a force
, acquires an acceleration of 1 m/s2. The mass of this
body must be:
1. 10 kg
2. 20 kg
3. 10 2 kg
4. 2 kg
The mass of a lift is 2000 kg. When the tension in the supporting cable is 28000 N, then its acceleration is:
1. 4 ms–2 upwards
2. 4 ms–2 downwards
3. 14 ms–2 upwards
4. 30 ms–2 downwards