Advertisements
Advertisements
प्रश्न
A girl riding a bicycle along a straight road with a speed of 5 ms–1 throws a stone of mass 0.5 kg which has a speed of 15 ms–1 with respect to the ground along her direction of motion. The mass of the girl and bicycle is 50 kg. Does the speed of the bicycle change after the stone is thrown? What is the change in speed, if so?
Advertisements
उत्तर
Given, the total mass of girl, bicycle and stone = m1 = (50 + 0.5) kg = 50.5 kg.
Velocity of bicycle u1 = 5 m/s, Mass of stone m2 = 0.5 kg
Velocity of stone u2 = 15 m/s, Mass of girl and bicycle m = 50 kg
Yes, the speed of the bicycle changes after the stone is thrown.
Let after throwing the stone the speed of bicycle is v ms.
According to the law of conservation of linear momentum,
m1u1 = m2u2 + mv
50.5 × 5 = 0.5 × 15 + 50 × v
252.5 – 7.5 = 50 v
or v = `245.0/50`
v = 4.9/m/s
Change in speed = 5 – 4.9 = 0.1 m/s.
APPEARS IN
संबंधित प्रश्न
Two objects, each of mass 1.5 kg are moving in the same straight line but in opposite directions. The velocity of each object is 2.5 m s−1 before the collision during which they stick together. What will be the velocity of the combined object after collision?
Akhtar, Kiran and Rahul were riding in a motorcar that was moving with a high velocity on an expressway when an insect hit the windshield and got stuck on the windscreen. Akhtar and Kiran started pondering over the situation. Kiran suggested that the insect suffered a greater change in momentum as compared to the change in momentum of the motorcar (because the change in the velocity of the insect was much more than that of the motorcar). Akhtar said that since the motorcar was moving with a larger velocity, it exerted a larger force on the insect. And as a result the insect died. Rahul while putting an entirely new explanation said that both the motorcar and the insect experienced the same force and a change in their momentum. Comment on these suggestions.
A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei the products must move in opposite directions.
Two billiard balls, each of mass 0.05 kg, moving in opposite directions with speed 6 ms-1collide and rebound with the same speed. What is the impulse imparted to each ball due to the other?
Figure shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating with 1 m s–2. What is the net force on the man? If the coefficient of static friction between the man’s shoes and the belt is 0.2, up to what acceleration of the belt can the man continue to be stationary relative to the belt? (Mass of the man = 65 kg.)
A stream of water flowing horizontally with a speed of 15 m s–1 gushes out of a tube of cross-sectional area 10–2 m2, and hits a vertical wall nearby. What is the force exerted on the wall by the impact of water, assuming it does not rebound?
What is the SI unit of momentum ?
What is the total momentum of the bullet and the gun before firing ?
Calculate the momentum of a toy car of mass 200 g moving with a speed of 5 m/s.
What is the momentum in kg.m/s of a 10 kg car travelling at (a) 5 m/s (b) 20 cm/s, and (c) 36 km/h ?
Which physical principle is involved in the working of a jet aeroplane ?
Name the principle on which a rocket works.
Fill in the following blanks with suitable words :
In collisions and explosions, the total _____________ remains constant, provided that no external _____________ acts.
A 10 g bullet travelling at 200 m/s strikes and remains embedded in a 2 kg target which is originally at rest but free to move. At what speed does the target move off ?
The velocity of a body of mass 10 kg increases from 4 m/s to 8 m/s when a force acts on it for 2 s.
(a) What is the momentum before the force acts ?
(b) What is the momentum after the force acts ?
(c) What is the gain in momentum per second ?
(d) What is the value of the force ?
Explain why it is possible for a small animal to fall from a considerable height without any injury being caused when it reaches the ground.
A ball X of mass 1 kg travelling at 2 m/s has a head-on collision with an identical ball Y at rest. X stops and Y moves off. Calculate the velocity of Y after the collision.
A 100 kg gun fires a ball of 1 kg horizontally from a cliff of height 500 m. It falls on the ground at a distance of 400 m from the bottom of the cliff. Find the recoil velocity of the gun. (acceleration due to gravity = 10 ms–2)
Two blocks P and Q of masses 0.3 kg and 0.4 kg, respectively, are stuck to each other by some weak glue as shown in the figure. They hang together at the end of a spring with a spring constant of k = 200 N/m. The block Q suddenly falls free due to the failure of glue, then the maximum kinetic energy of block P during subsequent motion will be ______ mJ.
