Advertisements
Advertisements
प्रश्न
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)
Advertisements
उत्तर
Given, the mass of the gun (m1) = 100
Mass of the ball (m2) = 1 kg
Height of the cliff = 500 m
Horizontal distance travelled by the ball (x) = 400 m
From `h = 1/2 "gt"^2` .....(∵ Initial velocity in the downward direction is zero)
`500 = 1/2 xx 10 t^2`
`t = sqrt(100)` = 10 s
From `x = ut, u = x/t = 400/10` = 40 m/s
It v is the recoil velocity of gun, then according to the principle of conservation of linear momentum,
m1v = m2u
v = `(m_2u)/m_1 = 1/100 xx 40` = 0.4 m/s
APPEARS IN
संबंधित प्रश्न
From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 m s−1. Calculate the initial recoil velocity of the rifle.
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.
Figure shows the position-time graph of a body of mass 0.04 kg. Suggest a suitable physical context for this motion. What is the time between two consecutive impulses received by the body ? What is the magnitude of each impulse ?
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?
Explain the meaning of the following equation : .
p = m x v
where symbols have their usual meanings.
Explain how, a karate player can break a pile of tiles with a single blow of his hand.
State the relation between the momentum of a body and the force acting on it.
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 ?
A gun of mass 3 kg fires a bullet of mass 30 g. The bullet takes 0.003 s to move through the barrel of the gun and acquires a velocity of 100 m/s. Calculate:
- the velocity with which the gin recoils.
- the force exerted on gunman due to recoil of the gun
Explain why, a cricket player moves his hands backwards while catching a fast cricket ball.
Discuss the conservation of momentum in each of the following cases :
(i) a rocket taking off from ground.
(ii) flying of a jet aeroplane.
An unloaded truck weighing 2000 kg has a maximum acceleration of 0.5 m/s2. What is the maximum acceleration when it is carrying a load of 2000 kg ?
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 heavy car A of mass 2000 kg travelling at 10 m/s has a head-on collision with a sports car B of mass 500 kg. If both cars stop dead on colliding, what was the velocity of car B ?
A man wearing a bullet-proof vest stands still on roller skates. The total mass is 80 kg. A bullet of mass 20 grams is fired at 400 m/s. It is stopped by the vest and falls to the ground. What is then the velocity of the man?
Suppose a ball of mass m is thrown vertically upward with an initial speed v, its speed decreases continuously till it becomes zero. Thereafter, the ball begins to fall downward and attains the speed v again before striking the ground. It implies that the magnitude of the initial and final momentums of the ball are the same. Yet, it is not an example of conservation of momentum. Explain why?
A monkey of mass 20 kg rides on a 40 kg trolley moving with constant speed of 8 m/s along a horizontal track If the monkey jumps vertically to grab the overhanging branch of a tree, the speed of the trolley after the monkey has jumped off is ______.
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.
