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question_answer1) An object is projected with a speed 10 m/s at an angle of \[30{}^\circ \]with the horizontal. The object breaks down into n equal fragments during its motion. One fragment is found to strike the ground at a distance of \[\sqrt{3}\]m from the point of projection in the same azimuthal plane, in which the object is projected. If the centre of mass of the remaining fragments strikes the ground at distance of \[7\sqrt{3}\]m from the point of projection, then the value of n is (all parts fall simultaneously on grounds)
question_answer2) Two spherical bodies of masses m and 5m and radii R and 2R respectively are released in free space with initial separation between their centres equal of 12R. If they attract each other due to gravitational force only then the distance covered by smaller sphere just before collisions will be nR. Then find value of n.
question_answer3) A machine gun fires 50 gm bullets at a speed of 1000 m/s. The gunner, holding the machine gun in his hands, can exert an average force of 180 newton against the gun. Determine the maximum number of bullets he can fire per minute.
question_answer4) A block of mass M is tied to one end of a massless rope. The other end of the rope is in the hands of a man of mass 2M as shown in the figure. The block and the man are resting on a rough wedge of mass M as shown in the figure. The whole system is resting on a smooth horizontal surface. The man pulls the rope. Pulley is massless and frictionless. What is the displacement (in m) of the wedge when the block meets the pulley? (Man does not leave his position during the pull) (on the block 2M.)
question_answer5) An inclined plane is placed on a horizontal smooth surface. The plane is struck by an small elastic ball whose velocity is horizontal just before the impact. The ball bounces off the inclined plane and then lands on it again at the point of first impact. Find the ratio of the masses of the ball and the inclined plane. (Angle \[\theta =30{}^\circ \])
question_answer6) Three objects A, B and C are kept in a straight line on a frictionless surface. These have masses m, 2m and 2m, respectively. The object A moves towards B with a speed 9 m/s and makes an elastic collision with it. Thereafter, B makes an elastic collision with C. All motions occur on the same straight line. The final speed (in m/s) of object B is found to be x. Find the value of 'x'.
question_answer7) Two point particles A and B are placed in line on a frictionless horizontal plane. If particle A (mass 1 kg) is moved with velocity 10 m/s towards stationary particle B (mass 2kg) and after collision they move at an angle of \[45{}^\circ \]with the initial direction of motion, then the velocity of particle B just after collision is found to be \[\frac{x}{\sqrt{2}}m/s\].
question_answer8) Two blocks of masses \[m\] and 2m are kept on a smooth horizontal surface. They are connected by an ideal spring of force constant \[k\]. Initially the spring is unstretched. A constant force F is applied to the heavier block in the direction shown in figure. Suppose at time \[t\] displacement of smaller block is \[x\], the displacement of the heavier block at this moment would be\[\left( \frac{F{{t}^{2}}}{Qm}-\frac{x}{2} \right)\]. Find the value of 'Q'.
question_answer9) Two particles of mass \[{{m}_{1}}\]and \[{{m}_{2}}\]start moving from point \[O\] with same constant speed\[{{v}_{0}}\], one is along + x-axis and other is along + y-axis. The particles are moving on smooth horizontal surface. The net linear momentum of the system of two particles as observed by the observer in the frame of centre of mass is found to be \[x\], find the value of \[x\].
question_answer10) Two smooth spheres A and B, of equal radius but mass m and M, are free to move on a horizontal table. A is projected with speed u towards B which is at rest. On impact, the line joining their centers is inclined at an angle θ to the velocity of A before impact. If e is the coefficient of restitution between the spheres If A's path after impact is perpendicular to its path before impact then coefficient of restitution is found to be 1/n, find n. [Given: m = 5kg, M = 10 kg,\[\theta =30{}^\circ \]]
question_answer11) Two identical smooth balls are projected from points O and A on the horizontal ground with same speed of projection. The angle of projection in each case is \[30{}^\circ \](see figure). The distance between O and A is 100m. The balls collide in mid air and return to their respective points of projection. If the coefficient of restitution is 0.7, the speed of projection of either ball (in m/s) correct to nearest integer is 19x m/s. Find x. (Take g = 10 \[m{{s}^{-2}}\]and \[\sqrt{3}\]= 1.7)
question_answer12) Three identical balls A, B and C each of mass m = 3 kg are connected by strings AB and BC as shown in the figure. The whole system is placed on a smooth horizontal surface. Now the ball B is given an initial velocity \[{{v}_{0}}=\sqrt{3}\] m/s, perpendicular to the string and along the horizontal surface. Find the tension (in Newton) in the string just before the balls A and C collide.
question_answer13) A ball of mass 1 kg moving with speed of 10 m/s on a smooth horizontal plane collides obliquely with another ball of same mass at rest as shown in the figure. Coefficient of restitution for the collision is 0.5. if the speed of the striking ball after the collision is \[\frac{35}{x}\]m/s, then x is
question_answer14) Board A is placed on board B as shown. Both boards slide, without moving with respect to each other, along a frictionless horizontal surface at a speed 6 m/s. Board B hits a resulting board C "head-on". After the collision, boards B and C stick together and board A slides on top of board C and stops its motion relative to C in the position shown on the diagram. What is the length (in m) of each board? All three boards have the same mass, size and shape. The coefficient of kinetic friction between boards A and C and between boards A&B is 0.3. (here g = 10 \[m/{{s}^{2}}\])
question_answer15) The friction coefficient between the horizontal surface and each of the block shown in the figure is 0.2. The collision between the blocks is perfectly elastic. Find the separation (in cm) between them when they come to rest. \[Take\text{ }g=10\,m/{{s}^{2}}\].
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Now the ball B is given an initial velocity \[{{v}_{0}}=\sqrt{3}\] m/s, perpendicular to the string and along the horizontal surface. Find the tension (in Newton) in the string just before the balls A and C collide. 
