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) $\frac{3}{2}v\mathrm{cos}\theta$

(4) $\frac{\sqrt{3}}{2}v\mathrm{cos}\theta$

Concept Questions :-

Linear momentum
High Yielding Test Series + Question Bank - NEET 2020

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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) $10\sqrt{2}\text{\hspace{0.17em}}m/second$ and 135° from either

(2) $10\sqrt{2}\text{\hspace{0.17em}}m/second$ and 45° from either

(3) $\frac{10}{\sqrt{2}}\text{\hspace{0.17em}}m/second$ and 135° from either

(4) $\frac{10}{\sqrt{2}}\text{\hspace{0.17em}}m/second$ and 45° from either

Concept Questions :-

Linear momentum
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Two particles of masses m1 and m2 in projectile motion have velocities ${\stackrel{\to }{v}}_{1}$ and ${\stackrel{\to }{v}}_{2}$ respectively at time t = 0. They collide at time t0. Their velocities become ${\stackrel{\to }{v}}_{1}\text{'}$ and ${\stackrel{\to }{v}}_{2}\text{'}$ at time 2t0 while still moving in air. The value of $\left|\left({m}_{1}\stackrel{\to }{{v}_{1}}\text{'}\text{\hspace{0.17em}}+{m}_{2}\stackrel{\to }{{v}_{2}}\text{'}\right)-\left({m}_{1}\stackrel{\to }{{v}_{1}}\text{\hspace{0.17em}}+{m}_{2}\stackrel{\to }{{v}_{2}}\right)\right|$ is

(1) Zero

(2) $\left({m}_{1}+{m}_{2}\right)g{t}_{0}$

(3) $2\left({m}_{1}+{m}_{2}\right)g{t}_{0}$

(4) $\frac{1}{2}\left({m}_{1}+{m}_{2}\right)g{t}_{0}$

Concept Questions :-

Linear momentum
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Difficulty Level:

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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Difficulty Level:

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 $\frac{T}{4}$, remains constant for a further time $\frac{T}{2}$ and decreases linearly from F0 to zero in further time $\frac{T}{4}$ as shown. The magnitude possessed by F0 is (1) $\frac{mu}{T}$

(2) $\frac{2mu}{T}$

(2) $\frac{4mu}{3T}$

(4) $\frac{3mu}{4T}$

Concept Questions :-

Linear momentum
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

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) 25$m/{s}^{2}$

(b) 0.25 $rad/{s}^{2}$

(c) 25 $rad/{s}^{2}$

(d) 5 $m/{s}^{2}$

Concept Questions :-

Torque
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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 . They are brought into contact face to face coinciding the axis of rotation.  The expression for loss of energy during this proces is

(a)$\frac{1}{2}I{\left({\omega }_{1}+{\omega }_{2}\right)}^{2}$

(b) $\frac{1}{4}I{\left({\omega }_{1}-{\omega }_{2}\right)}^{2}$

(c) $I{\left({\omega }_{1}-{\omega }_{2}\right)}^{2}$

(d) $\frac{1}{8}I{\left({\omega }_{1}-{\omega }_{2}\right)}^{2}$

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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Difficulty Level:

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
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

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