Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
According to the question, uranium 238 nucleus emits an alpha-particle with a speed of 1.4 × 107 m/s.
Let the speed of the residual nucleus thorium 234 be v2.
By the law of conservation of linear momentum, we have:
\[m_1 v_1 = m_2 v_2\]
Here, m1 and v1 are the mass and velocity of the alpha-particle repectively, and m2 is the mass of the residual nucleus.
\[\Rightarrow 4 \times 1 . 4 \times {10}^7 = 234 \times v_2 \]
\[ v_2 = \frac{4 \times 1 . 4 \times {10}^7}{234} = 2 . 4 \times {10}^5 \text{ m/s }\]
Therefore, the speed of the residual nucleus is
\[2 . 4 \times {10}^5 \text{ m/s}\]
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?
Two bodies make an elastic head-on collision on a smooth horizontal table kept in a car. Do you expect a change in the result if the car is accelerated in a horizontal road because of the non inertial character of the frame? Does the equation "Velocity of separation = Velocity of approach" remain valid in an accelerating car? Does the equation "final momentum = initial momentum" remain valid in the accelerating car?
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"?
A van is standing on a frictionless portion of a horizontal road. To start the engine, the vehicle must be set in motion in the forward direction. How can be persons sitting inside the van do it without coming out and pushing from behind?
A bullet hits a block kept at rest on a smooth horizontal surface and gets embedded into it. Which of the following does not 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.
In an elastic collision
(a) the kinetic energy remains constant
(b) the linear momentum remains constant
(c) the final kinetic energy is equal to the initial kinetic energy
(d) the final linear momentum is equal to the initial linear momentum.
A man of mass 50 kg starts moving on the earth and acquires a speed 1.8 m/s. With what speed does the earth recoil? Mass of earth = 6 × 1024 kg.
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 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.
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.
Two mass m1 and m2 are connected by a spring of spring constant k and are placed on a frictionless horizontal surface. Initially the spring is stretched through a distance x0 when the system is released from rest. Find the distance moved by the two masses before they again come to rest.
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.
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 metre stick is held vertically with one end on a rough horizontal floor. It is gently allowed to fall on the floor. Assuming that the end at the floor does not slip, find the angular speed of the rod when it hits the floor.
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 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?
