A block of mass M is kept on a smooth horizontal surface. A jet of water emerging from a nozzle of cross-section, it strikes the block horizontally with a speed u . Assuming ρ as the density of water. (i) Find the maximum power applied on the block. (ii) Calculate the thrust imparted by water jet on the block at this time. (ii) Obtain an expression for the speed of the block as the function of time.

(i) Let velocity of the block at any time be v . The thrust force on the block is F thrust = ρAv rel 2 = u - v 2 Aρ . . . . i The power due to impact force is P = F thrust . v = Aρv rel 2 · v = Aρ u - v 2 v . . . . ii For maximum power, dP dv = 0 or Aρ - v × 2 u - v + u - v 2 = 0 ⇒ v = u 3 The power applied on the block due to the thrust imparted by water jet on the block will be maximum when the velocity of the block reaches one third of water jet velocity. Putting v = u 3 , in Equation (i) and (ii) we get F thrust = 4 9 Aρu 2 and P max = 4 27 Aρu 3 (ii) The thrust force on the block is F thrust = ρAv rel 2 = u - v 2 Aρ u - v 2 Aρ = Mdv dt ∫ 0 v dv u - v 2 = Aρ M ∫ 0 t dt Which gives, v = u 1 + M Aρut

HARD

JEE Advanced

IMPORTANT

Earn 100

A rocket has initial velocity $v_{0}$ and mass $m_{0} .$ If it travels in free space, find the velocity of the rocket as the function of its existing mass $M .$ Assume that that rocket expels the fuel with a velocity $u_{r e l}$ with respect to itself.

Important Questions on Impulse and Collision

MEDIUM

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 2 - Impulse and Collision>CONCEPT APPLICATION EXERCISE>Q 7

A cart is pulled with a constant force $F$ with a constant velocity $v$ on a smooth horizontal ground. A Hooper loads the cart with sands at a time of $μ kg / s .$ Find the:

Question Image

(i) External force $F$
(ii) The power delivered by the external force.
(iii) The rate of change of kinetic energy.

MEDIUM

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 2 - Impulse and Collision>CONCEPT APPLICATION EXERCISE>Q 8

A block of mass $M$ is kept on a smooth horizontal surface. A jet of water emerging from a nozzle of cross-section, it strikes the block horizontally with a speed $u .$ Assuming $ρ$ as the density of water.

Question Image

(i) Find the maximum power applied on the block.
(ii) Calculate the thrust imparted by water jet on the block at this time.
(ii) Obtain an expression for the speed of the block as the function of time.

HARD

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 2 - Impulse and Collision>Exercises>Q 1

A ball impinges directly on a similar ball at rest. The first ball is brought to rest by the impact. If half of the energy is lost by impact, the value of co-efficient of restitution is

HARD

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 2 - Impulse and Collision>Exercises>Q 2

A particle of mass

2 kg

moving with a velocity of

3 m / s

is acted upon by a force which changes its direction of motion by an angle of

90 °

without changing its speed. What is the magnitude of impulse experienced by the particle?

MEDIUM

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 2 - Impulse and Collision>Exercises>Q 3

A body of mass

3 kg

is moving with a velocity of

4 m s^{- 1}

towards the right, collides head on with a body of mass

4 kg

moving in the opposite direction with a velocity of

3 m s^{- 1}

. After collision, the two bodies stick together and move with a common velocity, which is

HARD

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 2 - Impulse and Collision>Exercises>Q 4

A ball of mass $m$ moving with velocity $v_{0}$ collides with a wall as shown in figure. After impact it rebounds with a velocity $v_{0} / 2$ The component of impulse acting on the ball along the wall is

Question Image

MEDIUM

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 2 - Impulse and Collision>Exercises>Q 5

A particle of mass

m

moving with a velocity

u

makes an elastic one dimensional collision with a stationary particle of mass

m

establishing a contact with it for extremely small time

T

. Their force of contact increases from zero to

F_{0}

linearly in time

\frac{T}{4}

, remains constant for a further time

\frac{T}{2}

and decreases linearly from

F_{0}

to zero in further time

\frac{T}{4}

as shown in figure. The magnitude possessed by

F_{0}

is,

HARD

JEE Advanced

IMPORTANT

Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 2 - Impulse and Collision>Exercises>Q 6

A ball of mass

m

moving with speed

u

undergoes a head on elastic collision with a ball of mass

n m

initially‌ at rest. The fraction of the incident energy transferred to the second ball is :

A rocket has initial velocity v0 and mass m0. If it travels in free space, find the velocity of the rocket as the function of its existing mass M. Assume that that rocket expels the fuel with a velocity urel with respect to itself.

Important Questions on Impulse and Collision

Learn and Prepare for any exam you want !

A rocket has initial velocity $v_{0}$ and mass $m_{0} .$ If it travels in free space, find the velocity of the rocket as the function of its existing mass $M .$ Assume that that rocket expels the fuel with a velocity $u_{r e l}$ with respect to itself.