Advertisements
Advertisements
प्रश्न
A ball of mass 50 g moving at a speed of 2.0 m/s strikes a plane surface at an angle of incidence 45°. The ball is reflected by the plane at equal angle of reflection with the same speed. Calculate (a) the magnitude of the change in momentum of the ball (b) the change in the magnitude of the momentum of the ball.
Advertisements
उत्तर
It is given that:
Mass of the ball = 50 g =
\[0 . 05 \text{ Kg}\]
Speed of the ball, v = 2.0 m/s
Incident angle = 45˚
\[v = 2 \cos 45^\circ \hat i - 2 \sin 45^\circ \hat j \]
\[v' = - 2 \cos 45^\circ \hat i - 2 \sin 45^\circ \hat j\]
\[(a) \text{ Change in momentum } = m \vec{v} - m \vec{v} '\]
\[ = 0 . 05\left( 2 \cos 45^\circ\ \hat i - 2 \sin 45^\circ \hat j \right) - 0 . 05\left( - 2 \cos 45^\circ \hat i - 2 \sin 45^\circ \hat j \right)\]
\[ = 0 . 1 \cos 45^\circ\ \hat i - 0 . 1 \sin 45^\circ \ \hat j + 0 . 1 \cos 45^\circ \ \hat i + 0 . 1 \sin 45^\circ\ \hat j\]
\[ = 0 . 2 \cos 45^\circ\ \hat i \]
\[ \therefore \text{ Magnitude }= \frac{0 . 2}{\sqrt{2}} = 0 . 14 \text{ Kg m/s}\]
(b) The change in magnitude of the momentum of the ball,
\[\left| \vec{P}_2 \right| - \left| \vec{P}_1 \right| = 2 \times 0 . 5 - 2 \times 0 . 5 = 0\]
i.e. There is no change in magnitude of the momentum of the ball.
APPEARS IN
संबंधित प्रश्न
If the total mechanical energy of a particle is zero, is its linear momentum necessarily zero? Is it necessarily nonzero?
If the linear momentum of a particle is known, can you find its kinetic energy? If the kinetic energy of a particle is know can you find its linear momentum?
Suppose we define a quantity 'Linear momentum' as linear momentum = mass × speed.
The linear momentum of a system of particles is the sum of linear momenta of the individual particles. Can we state principle of conservation of linear momentum as "linear momentum of a system remains constant if no external force acts on it"?
When a nucleus at rest emits a beta particle, it is found that the velocities of the recoiling nucleus and the beta particle are not along the same straight line. How can this be possible in view of the principle of conservation of momentum?
Internal forces can change
A nucleus moving with a velocity \[\vec{v}\] emits an α-particle. Let the velocities of the α-particle and the remaining nucleus be v1 and v2 and their masses be m1 and m2.
A block moving in air breaks in two parts and the parts separate
(a) the total momentum must be conserved
(b) the total kinetic energy must be conserved
(c) the total momentum must change
(d) the total kinetic energy must change
A ball hits a floor and rebounds after an inelastic collision. In this case
(a) the momentum of the ball just after the collision is same as that just before the collision
(b) the mechanical energy of the ball remains the same during the collision
(c) the total momentum of the ball and the earth is conserved
(d) the total energy of the ball and the earth remains the same
A uranium-238 nucleus, initially at rest, emits an alpha particle with a speed of 1.4 × 107m/s. Calculate the recoil speed of the residual nucleus thorium-234. Assume that the mass of a nucleus is proportional to the mass number.
In a typical Indian Bugghi (a luxury cart drawn by horses), a wooden plate is fixed on the rear on which one person can sit. A bugghi of mass 200 kg is moving at a speed of 10 km/h. As it overtakes a school boy walking at a speed of 4 km/h, the boy sits on the wooden plate. If the mass of the boy is 25 kg, what will be the plate. If the mass of the boy is 25 kg, what will be the new velocity of the bugghi ?
A bullet of mass 20 g travelling horizontally with a speed of 500 m/s passes through a wooden block of mass 10.0 kg initially at rest on a level surface. The bullet emerges with a speed of 100 m/s and the block slides 20 cm on the surface before coming to rest. Find the friction coefficient between the block and the surface (See figure).
A block of mass 200 g is suspended through a vertical spring. The spring is stretched by 1.0 cm when the block is in equilibrium. A particle of mass 120 g is dropped on the block from a height of 45 cm. The particle sticks to the block after the impact. Find the maximum extension of the spring. Take g = 10 m/s2.
Two blocks of masses m1 and m2 are connected by a spring of spring constant k (See figure). The block of mass m2 is given a sharp impulse so that it acquires a velocity v0 towards right. Find (a) the velocity of the centre of mass, (b) the maximum elongation that the spring will suffer.
The blocks shown in figure have equal masses. The surface of A is smooth but that of Bhas a friction coefficient of 0.10 with the floor. Block A is moving at a speed of 10 m/s towards B which is kept at rest. Find the distance travelled by B if (a) the collision is perfectly elastic and (b) the collision is perfectly inelastic.
A uniform rod pivoted at its upper end hangs vertically. It is displaced through an angle of 60° and then released. Find the magnitude of the force acting on a particle of mass dm at the tip of the rod when the rod makes an angle of 37° with the vertical.
A small disc is set rolling with a speed \[\nu\] on the horizontal part of the track of the previous problem from right to left. To what height will it climb up the curved part?
A sphere starts rolling down an incline of inclination θ. Find the speed of its centre when it has covered a distance l.
A thin spherical shell of radius R lying on a rough horizontal surface is hit sharply and horizontally by a cue. Where should it be hit so that the shell does not slip on the surface?
The track shown is figure is frictionless. The block B of mass 2m is lying at rest and the block A or mass m is pushed along the track with some speed. The collision between Aand B is perfectly elastic. With what velocity should the block A be started to get the sleeping man awakened?
