Advertisements
Advertisements
प्रश्न
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.
विकल्प
\[\vec{v} , \vec{v}_1 \text{ and } \vec{v}_2\] must be parallel to each other.
None of the two of \[\vec{v} , \vec{v}_1 \text{ and } \vec{v}_2\] should be parallel to each other.
\[\vec{v_1} + \vec{v_2}\] must be parallel to \[\vec{v}\]
\[m_1 \vec{v_1} + m_2 \vec{v_2}\] must be parallel to \[\vec{v}\]
Advertisements
उत्तर
\[m_1 \vec{v_1} + m_2 \vec{v_2}\] must be parallel to \[\vec{v}\]
By the law of conservation of linear momentum, we can write:
\[\text{ Initial momentum } = \text{ Final momentum }\]
\[ \Rightarrow m \vec{v} = m_1 \vec{v}_1 + m_2 \vec{v}_2 \]
\[ \Rightarrow ( m_1 \vec{v}_1 + m_2 \vec{v}_2 ) \text{ must be parallel to } \vec{v}\]
APPEARS IN
संबंधित प्रश्न
A bob suspended from the ceiling of a car which is accelerating on a horizontal road. The bob stays at rest with respect to the car with the string making an angle θ with the vertical. The linear momentum of the bob as seen from the road is increasing with time. Is it a violation of conservation of linear momentum? If not, where is the external force changes the linear momentum?
If the total mechanical energy of a particle is zero, is its linear momentum necessarily zero? Is it necessarily nonzero?
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"?
Consider the following two statements:
(A) Linear momentum of a system of particles is zero.
(B) Kinetic energy of a system of particles is zero.
Internal forces can change
The quantities remaining constant in a collisions are
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 man of mass M having a bag of mass m slips from the roof of a tall building of height H and starts falling vertically in the following figure. When at a height h from the ground, the notices that the ground below him is pretty hard, but there is a pond at a horizontal distance x from the line of fall. In order to save himself he throws the bag horizontally (with respect to himself) in the direction opposite to the pond. Calculate the minimum horizontal velocity imparted to the bag so that the man lands in the water. If the man just succeeds to avoid the hard ground, where will the bag land?
A gun is mounted on a railroad car. The mass of the car, the gun, the shells and the operator is 50 m where m is the mass of one shell. If the velocity of the shell with respect to the gun (in its state before firing) is 200 m/s, what is the recoil speed of the car after the second shot? Neglect friction.
A 60 kg man skating with a speed of 10 m/s collides with a 40 kg skater at rest and they cling to each other. Find the loss of kinetic energy during the collision.
A ball of mass m moving at a speed v makes a head-on collision with an identical ball at rest. The kinetic energy of the balls after the collision is three fourths of the original. Find the coefficient of restitution.
A bullet of mass 25 g is fired horizontally into a ballistic pendulum of mass 5.0 kg and gets embedded in it. If the centre of the pendulum rises by a distance of 10 cm, find the speed of the bullet.
A bullet of mass 20 g moving horizontally at a speed of 300 m/s is fired into a wooden block of mass 500 g suspended by a long string. The bullet crosses the block and emerges on the other side. If the centre of mass of the block rises through a height of 20.0 cm, find the speed of the bullet as it emerges from the block.
The friction coefficient between the horizontal surface and each of the block shown in figure is 0.20. The collision between the blocks is perfectly elastic. Find the separation between the two blocks when they come to rest. Take g = 10 m/s2.
A small block of superdense material has a mass of 3 × 1024kg. It is situated at a height h (much smaller than the earth's radius) from where it falls on the earth's surface. Find its speed when its height from the earth's surface has reduce to to h/2. The mass of the earth is 6 × 1024kg.
A sphere starts rolling down an incline of inclination θ. Find the speed of its centre when it has covered a distance l.
A solid sphere of mass m is released from rest from the rim of a hemispherical cup so that it rolls along the surface. If the rim of the hemisphere is kept horizontal, find the normal force exerted by the cup on the ball when the ball reaches the bottom of the cup.
The following figure shows a rough track, a portion of which is in the form of a cylinder of radius R. With what minimum linear speed should a sphere of radius r be set rolling on the horizontal part so that it completely goes round the circle on the cylindrical part.
