A shell is fired from a cannon with velocity v m/sec at an angle θ with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon. The speed (in m/sec) of the other piece immediately after the explosion is 

(1) 3v cos θ

(2) 2v cos θ

(3) 32vcosθ

(4) 32vcosθ

Concept Questions :-

Linear momentum
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A vessel at rest explodes into three pieces. Two pieces having equal masses fly off perpendicular to one another with the same velocity 30 meter per second. The third piece has three times mass of each of other piece. The magnitude and direction of the velocity of the third piece will be 

(1) 102m/second and 135° from either

(2) 102m/second and 45° from either

(3) 102m/second and 135° from either

(4) 102m/second and 45° from either

Concept Questions :-

Linear momentum
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Two particles of masses m1 and m2 in projectile motion have velocities v1 and v2 respectively at time t = 0. They collide at time t0. Their velocities become v1' and v2' at time 2t0 while still moving in air. The value of (m1v1'+m2v2')(m1v1+m2v2) is 

(1) Zero

(2) (m1+m2)gt0

(3) 2(m1+m2)gt0

(4) 12(m1+m2)gt0

Concept Questions :-

Linear momentum
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Consider elastic collision of a particle of mass m moving with a velocity u with another particle of the same mass at rest. After the collision the projectile and the struck particle move in directions making angles θ1 and θ2 respectively with the initial direction of motion. The sum of the angles. θ1 + θ2, is 

(1) 45°

(2) 90°

(3) 135°

(4) 180°

Concept Questions :-

Linear momentum
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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 T4, remains constant for a further time T2 and decreases linearly from F0 to zero in further time T4 as shown. The magnitude possessed by F0 is

(1) muT

(2) 2muT

(2) 4mu3T

(4) 3mu4T

Concept Questions :-

Linear momentum
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A rope is wound around a hollow cylinder of mass 3 kg and radius 40cm. What is the angular acceleration of the cylinder,if the rope is pulled with a force of 30 N?

(a) 25m/s2

(b) 0.25 rad/s2

(c) 25 rad/s2

(d) 5 m/s2

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Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ω1  and ω2. They are brought into contact face to face coinciding the axis of rotation.  The expression for loss of energy during this proces is 

(a)12Iω1+ω22

(b) 14Iω1-ω22

(c) Iω1-ω22

(d) 18Iω1-ω22 

Concept Questions :-

Angular momentum
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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 

(a) mv

(b) 2mv

(c) mv/2

(d) mv/3

Concept Questions :-

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

(a) 100 m/s 

(b) 80 m/s

(c) 120 m/s 

(d) 160 m/s 

 

Concept Questions :-

Linear momentum
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Two identical balls A and B having velocities of 0.5 m/s and -0.3 m/s respectively collide elastically in one dimension. The velocities of B and A after the collision respectively will be 

(a) -0.5 m/s and 0.3 m/s 

(b) 0.5 m/s and -0.3 m/s 

(c) -0.3 m/s and 0.5 m/s 

(d) 0.3 m/s and 0.5 m/s 

Concept Questions :-

Linear momentum
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