Advertisements
Advertisements
प्रश्न
A batsman deflects a ball by an angle of 45° without changing its initial speed which is equal to 54 km/h. What is the impulse imparted to the ball? (Mass of the ball is 0.15 kg.)
Advertisements
उत्तर
The given situation can be represented as shown in the following figure.
Where,
AO = Incident path of the ball
OB = Path followed by the ball after deflection
∠AOB = Angle between the incident and deflected paths of the ball = 45°
∠AOP = ∠BOP = 22.5° = θ
Initial and final velocities of the ball = v
Initial velocity's horizontal component = vcos θ along RO
Initial velocity's vertical component = vsin θ along PO
Final velocity's horizontal component = vcos θ along OS
Final velocity's vertical component = vsin θ along OP
The horizontal velocity components remain unchanged. The vertical velocity components are directed oppositely.
∴Impulse imparted to the ball = Change in the linear momentum of the ball
`= mvcostheta - (- mvcos theta)`
`= 2mvcos theta`
Mass of the ball, m = 0.15 kg
Velocity of the ball, v = 54 km/h = 15 m/s
∴ Impulse = 2 × 0.15 × 15 cos 22.5° = 4.16 kg m/s
APPEARS IN
संबंधित प्रश्न
You are travelling in a car. The driver suddenly applies the brakes and you are pushed forward. Why does this happen?
A smooth wedge A is fitted in a chamber hanging from a fixed ceiling near the earth's surface. A block B placed at the top of the wedge takes time T to slide down the length of the wedge. If the block is placed at the top of the wedge and the cable supporting the chamber is broken at the same instant, the block will.
In a TV picture tube, electrons are ejected from the cathode with negligible speed and they attain a velocity of 5 × 106 m/s in travelling one centimetre. Assuming straight-line motion, find the constant force exerted on the electrons. The mass of an electron is 9.1 × 10−31 kg.
A block of mass 0.2 kg is suspended from the ceiling by a light string. A second block of mass 0.3 kg is suspended from the first block by another string. Find the tensions in the two strings. Take g = 10 m/s2.
Both the springs shown in the following figure are unstretched. If the block is displaced by a distance x and released, what will be the initial acceleration?
Suppose the ceiling in the previous problem is that of an elevator which is going up with an acceleration of 2.0 m/s2. Find the elongation.
The force of buoyancy exerted by the atmosphere on a balloon is B in the upward direction and remains constant. The force of air resistance on the balloon acts opposite the direction of velocity and is proportional to it. The balloon carries a mass M and is found to fall to the earth's surface with a constant velocity v. How much mass should be removed from the balloon so that it may rise with a constant velocity v?
Let m1 = 1 kg, m2 = 2 kg and m3 = 3 kg in the following figure. Find the accelerations of m1, m2 and m3. The string from the upper pulley to m1 is 20 cm when the system is released from rest. How long will it take before m1 strikes the pulley?
Find the acceleration of the block of mass M in the situation shown in the following figure. All the surfaces are frictionless and the pulleys and the string are light.
A monkey is climbing on a rope that goes over a smooth light pulley and supports a block of equal mass at the other end in the following figure. Show that whatever force the monkey exerts on the rope, the monkey and the block move in the same direction with equal acceleration. If initially both were at rest, their separation will not change as time passes.
Two bodies A and B of same mass are moving with velocities v and 2v, respectively. Compare their (i) inertia and (ii) momentum.
The linear momentum of a ball of mass 50 g is 0.5 kg m s-1. Find its velocity.
A force acts for 10 s on a stationary body of mass 100 kg, after which the force ceases to act. The body moves through a distance of 100 m in the next 5 s. Calculate : The magnitude of the force
Multiple Choice Question. Select the correct option.
Which of the following are vector quantities?
A ball is thrown vertically downward with an initial velocity of 10 m/s. What is its speed 1 s later and 2 s later?
A stone is dropped from a tower 98 m high. With what speed should a second stone be thrown 1 s later so that both hit the ground at the same time?
A body of mass 2 kg travels according to the law x(t) = pt + qt2 + rt3 where p = 3 ms−1, q = 4 ms−2 and r = 5 ms−3. The force acting on the body at t = 2 seconds is ______.
A woman throws an object of mass 500 g with a speed of 25 ms1.
- What is the impulse imparted to the object?
- If the object hits a wall and rebounds with half the original speed, what is the change in momentum of the object?
What happens when a car brakes to come to a stop?
How does moving your hand backward while catching a cricket ball reduce pain?
