Advertisements
Advertisements
प्रश्न
Solve the following problem.
A spring ball of mass 0.5 kg is dropped from some height. On falling freely for 10 s, it explodes into two fragments of mass ratio 1:2. The lighter fragment continues to travel downwards with a speed of 60 m/s. Calculate the kinetic energy supplied during the explosion.
उत्तर
m1 + m2 = 0.5 kg, m1 : m2 = 1 : 2,
m1 = `1/6` kg
∴ m2 = `1/3` kg
Initially, when the ball is falling freely for 10s,
v = u + at = 0 + 10(10)
∴ v = 100 m/s = u1 = u2
(m1 + m2)v = m1v1 + m2v2
∴ `0.5 xx 100 = 1/6(60) + 1/3 "v"_2`
∴ 50 = 10 + `1/3 "v"_2`
∴ 40 = `1/3 "v"_2`
∴ v2 = 120 m/s
∴ Δ K.E. = `1/2 "m"_1"v"_1^2 + 1/2"m"_2"v"_2^2 - 1/2 ("m"_1 + "m"_2)"u"^2`
∴ Δ K.E. = `1/2(1/6) xx 60^2 + 1/2 xx 1/3 xx (120)^2 - 1/2 xx 0.5 xx (100)^2`
= 300 + 2400 - 2500
∴ K.E. = 200 J
Kinetic energy supplied is 200 J.
APPEARS IN
संबंधित प्रश्न
State if the following statement is true or false. Give a reason for your answer.
In an elastic collision of two bodies, the momentum and energy of each body is conserved.
State if the following statement is true or false. Give a reason for your answer.
In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system.
Answer carefully, with reason:
In an inelastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e., when they are in contact)?
Answer carefully, with reason:
If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic? (Note, we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy.)
The bob A of a pendulum released from 30° to the vertical hits another bob B of the same mass at rest on a table, as shown in the figure. How high does the bob A rise after the collision? Neglect the size of the bobs and assume the collision to be elastic.
Answer the following question.
Obtain its value for an elastic collision and a perfectly inelastic collision.
Solve the following problem.
A marble of mass 2m travelling at 6 cm/s is directly followed by another marble of mass m with double speed. After a collision, the heavier one travels with the average initial speed of the two. Calculate the coefficient of restitution.
Explain the characteristics of elastic and inelastic collision.
Define the following:
Coefficient of restitution
Arrive at an expression for elastic collision in one dimension and discuss various cases.
Two different unknown masses A and B collide. A is initially at rest when B has a speed v. After collision B has a speed v/2 and moves at right angles to its original direction of motion. Find the direction in which A moves after the collision.
In Rutherford experiment, for head-on collision of a-particles with a gold nucleus, the impact parameter is ______.
A block of mass 'm' moving on a frictionless surface at speed 'v' collides elastically with a block of same mass, initially at rest. Now the first block moves at an angle 'θ' with its initial direction and has speed 'v1'. The speed of the second block after collision is ______.
A ball of mass 0.1 kg makes an elastic head-on collision with a ball of unknown mass, initially at rest. If the 0 .1 kg ball rebounds at one-third of its original speed, the mass of the other ball is ______.
A bomb of mass 9 kg explodes into two pieces of mass 3 kg and 6 kg. The velocity of mass 3 kg is 16 m/s, The kinetic energy of mass 6 kg is ____________.
A mass M moving with velocity 'v' along x-axis collides and sticks to another mass 2M which is moving along Y-axis with velocity 3v. After collision, the velocity of the combination is ______.
A wooden block of mass 'M' moves with velocity 'v ' and collides with another block of mass '4M' which is at rest. After collision, the block of mass 'M' comes to rest. The coefficient of restitution will be ______.
A smooth sphere of mass 'M' moving with velocity 'u' directly collides elastically with another sphere of mass 'm' at rest. After collision, their final velocities are V' and V respectively. The value of V is given by ______.
During inelastic collision between two bodies, which of the following quantities always remain conserved?
Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed V as shown in figure.
If the collision is elastic, which of the following (Figure) is a possible result after collision?
A ball of mass m, moving with a speed 2v0, collides inelastically (e > 0) with an identical ball at rest. Show that for a general collision, the angle between the two velocities of scattered balls is less than 90°.
A particle of mass m with an initial velocity u`hat"i"` collides perfectly elastically with a mass 3m at rest. It moves with a velocity v`hat"j"` after collision, then, v is given by :
A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps forward and 3 steps backward, and so on. Each step is 1 m long and required 1 s to cover. How long the drunkard takes to fall in a pit 13 m away from the start?
The dimension of mutual inductance is ______.
Three identical blocks A, B and C are placed on horizontal frictionless surface. The blocks A and C are at rest. But A is approaching towards B with a speed 10 m/s. The coefficient of restitution for all collision is 0.5. The speed of the block C just after the collision is ______.
Answer carefully, with reason:
Is the total linear momentum conserved during the short time of an inelastic collision of two balls ?
