Given the masses of various atomic particles m P = 1 , 0072 u , m n = 1 , 0087 u , m e = 0 .000548 u , m v ¯ = 0 , m d = 2 .0141 u , where p = proton, n ≡ neutron, e ≡ electron, v ¯ ≡ antineutrino and d ¯ ≡ deuteron. Which of the following process is allowed by momentum and energy conservation :

n + n → deuterium atom (electron bound to the nucleus)

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A jet engine works on the principle of

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Important Questions on Newton's Laws of Motion

MEDIUM

Physics>Mechanics>Newton's Laws of Motion>Impulse and Conservation of Momentum

A block of mass $m = 1 kg$ slides with velocity $v = 6 m s^{- 1}$ on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about $O$ and swings as a result of the collision making angle $θ$ before momentarily coming to rest. if the rod has mass $M = 2 kg,$ and length $ℓ = 1 m,$ the value of $θ$ is approximately $(take g = 10 m s^{- 2})$

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HARD

Physics>Mechanics>Newton's Laws of Motion>Impulse and Conservation of Momentum

A man (mass

= 50 k g

) and his son (mass

= 20 k g

) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of

0.70 m s^{- 1}

with respect to the man. The speed of the man with respect to the surface is:

MEDIUM

Physics>Mechanics>Newton's Laws of Motion>Impulse and Conservation of Momentum

A block of mass m attached to a massless spring is performing oscillatory motion of amplitude 'A' on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become ƒA. The value of ƒ is:

HARD

Physics>Mechanics>Newton's Laws of Motion>Impulse and Conservation of Momentum

An object of mass

5 kg

is projected with a velocity

20 m s^{- 1}

at an angle

60 °

, to the horizontal. At the highest point of its path, the projectile explodes and breaks up into two fragments of masses

1 kg

and

4 kg .

The fragments separate horizontally after the explosion, which releases internal energy such that the

K E

of the system af the highest point is doubled. The separation between the two fragments when they reach the ground is

HARD

Physics>Mechanics>Newton's Laws of Motion>Impulse and Conservation of Momentum

A jeweler is holding a gold chain of uniform mass per unit length hanging vertically just above a weighing scale as shown in the figure. He offers to charge the customer for half of the maximum reading of the scale, after he releases the chain. What percentage more than the actual price does the customer pay if he agrees to the offer?

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HARD

Physics>Mechanics>Newton's Laws of Motion>Impulse and Conservation of Momentum

A man holding a rifle (mass of person and rifle together is

100 kg

) stands on a smooth surface and fires

10

shots horizontally in

5 \sec

. Each bullet has a mass

10 g

with a muzzle velocity of

800 m s^{- 1} .

The velocity which the rifle man attains after firing

10

shots will be

EASY

Physics>Mechanics>Newton's Laws of Motion>Impulse and Conservation of Momentum

Two particles which are initially at rest move towards each other under the action of their mutual attraction. If their speeds are

v

and

2 v

at any instant, then the speed of center of mass of the system is,

MEDIUM

Physics>Mechanics>Newton's Laws of Motion>Impulse and Conservation of Momentum

A ball of mass $10 kg$ moving with a velocity $10 \sqrt{3} {m s}^{- 1}$ along $X$ -axis, hits another ball of mass $20 kg$ which is at rest. After the collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along $Y$ -axis at a speed of $10 m s^{- 1}$ . The second piece starts moving at a speed of $20 m s^{- 1}$ at an angle $θ$ (degree) with respect to the $X$ -axis. The configuration of pieces after the collision is shown in the figure. The value of $θ$ (in degrees) to the nearest integer is _________.

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EASY

Physics>Mechanics>Newton's Laws of Motion>Impulse and Conservation of Momentum

A balloon has mass of

10 g

in air. The air escapes from the balloon at a uniform rate with velocity

4.5 cm s^{- 1}

. If the balloon shrinks in

5 s

completely. Then, the average force acting on that balloon will be (in dyne).

HARD

Physics>Mechanics>Newton's Laws of Motion>Impulse and Conservation of Momentum

A particle of mass

m

is projected from the ground with an initial speed

u_{\circ}

at an angle

α

with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed

u_{\circ}

. The angle that the composite system makes with the horizontal immediately after the collision is

MEDIUM

Physics>Mechanics>Newton's Laws of Motion>Impulse and Conservation of Momentum

A trolley having mass of

200 kg

moves with uniform speed of

36 {kmh}^{- 1}

on a frictionless track. A child of mass

20 kg

runs on the trolley from one end to the other (

10 m

away) with a speed of

4 m s^{- 1}

relative to the trolley in a direction opposite to its motion and ultimately jumps out of the trolley. With how much velocity has the trolley moved from the time the child begins to run?

MEDIUM

Physics>Mechanics>Newton's Laws of Motion>Impulse and Conservation of Momentum

A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate

\frac{d M (t)}{d t} = b v^{2} (t),

where

v (t)

is its instantaneous velocity. The instantaneous acceleration of the satellite is:

MEDIUM

Physics>Mechanics>Newton's Laws of Motion>Impulse and Conservation of Momentum

A stationary body explodes into two parts of masses

M_{1}

and

M_{2}

. They move in opposite directions with velocities

v_{1}

and

v_{2}

. The ratio of their kinetic energies is

MEDIUM

Physics>Mechanics>Newton's Laws of Motion>Impulse and Conservation of Momentum

Given the masses of various atomic particles

m_{P} = 1, 0072 u

m_{n} = 1, 0087 u

m_{e} = 0 .000548 u

m_{\bar{v}} = 0

m_{d} = 2 .0141 u

, where

p =

proton,

n \equiv

neutron,

e \equiv

electron,

\bar{v} \equiv

antineutrino and

\bar{d} \equiv

deuteron. Which of the following process is allowed by momentum and energy conservation :

MEDIUM

Physics>Mechanics>Newton's Laws of Motion>Impulse and Conservation of Momentum

A bomb of mass

18 kg

at rest explodes into two pieces of masses

6 kg

and

12 kg .

The velocity of

12 kg

mass is

4 m / s .

The kinetic energy of the other mass is

EASY

Physics>Mechanics>Newton's Laws of Motion>Impulse and Conservation of Momentum

A ball of mass $10 kg$ moving with a velocity $10 \sqrt{3} m s^{- 1}$ along the $x$ -axis, hits another ball of mass $20 kg$ which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along $y$ -axis with a speed of $10 m s^{- 1} .$ The second piece starts moving at an angle of $30 °$ with respect to the $x$ -axis. The velocity of the ball moving at $30 °$ with $x$ -axis is $x m s^{- 1} .$ The configuration of pieces after the collision is shown in the figure below. The value of $x$ to the nearest integer is

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EASY

Physics>Mechanics>Newton's Laws of Motion>Impulse and Conservation of Momentum

An object of mass

m_{1}

collides with another object of mass

m_{2}

, which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses

m_{2} : m_{1}

is :

MEDIUM

Physics>Mechanics>Newton's Laws of Motion>Impulse and Conservation of Momentum

A body of mass

(4 m)

is lying in

x

y

plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass

(m)

move perpendicular to each other with equal speeds

(υ) .

The total kinetic energy generated due to explosion is:

EASY

Physics>Mechanics>Newton's Laws of Motion>Impulse and Conservation of Momentum

A balloon has a mass of

10

gram in air. The air escapes from the balloon at a uniform rate with a velocity of

5 cm s^{- 1}

and the balloon shrinks completely in

2.5 s

. The average force acting on the balloon will be

EASY

Physics>Mechanics>Newton's Laws of Motion>Impulse and Conservation of Momentum

5000 kg

rocket is set for vertical firing. The exhaust speed is

800 m s^{- 1}

. To give an initial upward acceleration of

20 m s^{- 2}

, the amount of gas ejected per second to supply the needed thrust will be:

(g = 10 m s^{- 2})

A jet engine works on the principle of

Important Questions on Newton's Laws of Motion

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