Consider the following two statements
1. Linear momentum of a system of particles is zero
2. Kinetic energy of a system of particles is zero Then
(1) 1 implies 2 and 2 implies 1
(2) 1 does not imply 2 and 2 does not imply 1
(3) 1 implies 2 but 2 does not imply 1
(4) 1 does not imply 2 but 2 implies 1
A force-time graph for a linear motion is shown in figure where the segments are circular. The linear momentum gained between zero and 8 second is
1.
2.
3.
4.
A particle of mass m moving with a velocity u makes an elastic one dimensional collision with a stationary particle of mass m establishing a contact with it for extremely small time T. Their force of contact increases from zero to F0 linearly in time , remains constant for a further time and decreases linearly from F0 to zero in further time as shown. The magnitude possessed by F0 is
(1)
(2)
(2)
(4)
Two blocks A and B of masses 3m and m respectively are connected by a massless and inextenisible 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
1.
2.
3.
4.
One end of the 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 a circle with speed \(v\), the net force on the particle (directed towards the centre) will be: (\(T\) represents the tension in the string)
1. | \(T \) | 2. | \(T+\frac{m v^2}{l} \) |
3. | \(T-\frac{m v^2}{l} \) | 4. | \(\text{zero}\) |
A rigid ball of mass m strikes a rigid wall at 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
(1) mv
(2) 2mv
(3) mv/2
(4) mv/3
A car is negotiating a curved road of radius R. The road is banked at angle . The coefficient of friction between the tyres of the car and the road is . The maximum safe velocity on this road is
1.
2.
3.
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
1.2N
2. 6N
3. 8N
4. 18N
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 the table is μk. When the block A is sliding on the table, the tension in the string is
1. (m2+μkm1)g /(m1+m2)
2. (m2-μkm1)g/(m1+m2)
3. m1m2(1+μk)g/(m1+m2)
4. m1m2(1-μk)g/(m1+m2)
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 30°, 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. 0.6 and 0.6
2. 0.6 and 0.5
3. 0.5 and 0.6
4. 0.4 and 0.3