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.
Mass of the rifle, m1 = 4 kg
Mass of the bullet, m2 = 50g = 0.05 kg
Recoil velocity of the rifle = v1
Bullet is fired with an initial velocity, v2 = 35 m/s
Total mass = m1 + m2 = 4 + 0.05 = 4.05 kg
Since the system was at rest , velocity (v) = 0
Momentum ( before firing ) = mass x velocity = ( m1 + m2 )v = ( 4.05 ) 0 = 0 kg m/s
Total momentum = momentum of bullet + momentum of rifle = m1 v1 + m2 v2
= 0.05 x 35 + 4 x v2 = 7/4 + 4 v2
Since the total momentum remain conserved
Total momentum before firing = Total momentum after firing
0 = 7/4 + 4 v2
4 v2 = - 7/4
v2 = - 7/16
v2 = -04375 m/s
Thus , the recoil velocity of the pistol is -0.4375 m/s .
The negative sign of velocity means that the rifle will recoil in the opposite direction of the bullet.
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?
Two objects of masses 100 g and 200 g are moving along the same line and direction with velocities of 2 m s-1 and 1 m s-1, respectively. They collide and after the collision, the first object moves at a velocity of 1.67 m s-1. Determine the velocity of the second object.
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 hammer of mass 500 g, moving at 50 m s-1, strikes a nail. The nail stops the hammer in a very short time of 0.01 s. What is the force of the nail on the hammer?
A hockey ball of mass 200 g travelling at 10 m s-1 is struck by a hockey stick so as to return it along its original path with a velocity at 5 m s-1. Calculate the change of momentum occurred in the motion of the hockey ball by the force applied by the hockey stick.
A bullet of mass 10 g travelling horizontally with a velocity of 150 m s-1 strikes a stationary wooden block and comes to rest in 0.03 s. Calculate the distance of penetration of the bullet into the block. Also calculate the magnitude of the force exerted by the wooden block on the bullet.
A motorcar of mass 1200 kg is moving along a straight line with a uniform velocity of 90 km/h. Its velocity is slowed down to 18 km/h in 4 s by an unbalanced external force. Calculate the acceleration and change in momentum. Also calculate the magnitude of the force required.
Explain why some of the leaves may get detached from a tree if we vigorously shake its branch.
A truck starts from rest and rolls down a hill with a constant acceleration. It travels a distance of 400 m in 20 s. Find its acceleration. Find the force acting on it if its mass is 7 metric tonnes (Hint: 1 metric tonne = 1000 kg.)
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State the universal law of gravitation.
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Chair, air, love, smell, hate, almonds, thought, cold, cold-drink, smell of perfume.
A force of 7 N acts on an object. The displacement is, say 8 m, in the direction of the force (Fig. 11.3). Let us take it that the force acts on the object through the displacement. What is the work done in this case?
What is meant by a pure substance?
How does the sound produced by a vibrating object in a medium reach your ear?
In a reaction, 5.3 g of sodium carbonate reacted with 6 g of ethanoic acid. The products were 2.2 g of carbon dioxide, 0.9 g water and 8.2 g of sodium observations are in agreement with the law of conservation of mass.
sodium carbonate + ethanoic acid → sodium ethanoate + carbon dioxide + water
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If number of electrons in an atom is 8 and number of protons is also 8, then (i) what is the atomic number of the atom? and (ii) what is the charge on the atom?
The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy? Why?
Why do organisms need water?
Differentiate between parenchyma, collenchyma and sclerenchyma on the basis of their cell wall.
How are pteridophytes different from the phanerogams?
Under which of the following conditions is a person most likely to fall sick?
(a) when she is recovering from malaria.
(b) when she has recovered from malaria and is taking care of someone suffering from chicken-pox.
(c) when she is on a four-day fast after recovering from malaria and is taking care of someone suffering from chicken-pox. Why?
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Name the following.
(a) Tissue that forms the inner lining of our mouth.
(b) Tissue that connects muscle to bone in humans.
(c) Tissue that transports food in plants.
(d) Tissue that stores fat in our body.
(e) Connective tissue with a fluid matrix.
(f) Tissue present in the brain.