A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the x - axis. Its kinetic energy changes with time as d K d t = γ t , where γ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

The distance of the particle from the origin increases linearly with time

HARD

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The system shown adjacent is in equilibrium. Blocks $A, B & C$ are of equal masses $m$ (Assume springs to be ideal).

Then choose the correct statements.

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Important Questions on Laws of Motion

MEDIUM

Physics>Mechanics>Laws of Motion>Newton’s Laws of Motion

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} m^{2}

and hits a vertical wall nearby. The force exerted on the wall by the impact of water (assuming it does not rebound) is

EASY

Physics>Mechanics>Laws of Motion>Newton’s Laws of Motion

A mass $m$ is attached to two springs as shown in figure. The spring constants of two springs are $K_{1}$ and $K_{2} .$ For the frictionless surface, the time period of oscillation of mass $m$ is

Question Image

HARD

Physics>Mechanics>Laws of Motion>Newton’s Laws of Motion

A particle of mass

m

is initially at rest at the origin. It is subjected to a force and starts moving along the x - axis. Its kinetic energy changes with time as

\frac{d K}{d t} = γ t,

where

γ

is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

MEDIUM

Physics>Mechanics>Laws of Motion>Newton’s Laws of Motion

An elevator of mass

m

is connected to a rope which pulls the elevator up with a maximum acceleration equal to

a

. If the maximum bearable tension in the rope is

T

, then for a safe journey the minimum diameter of the rope is [

g

= acceleration due to gravity]

HARD

Physics>Mechanics>Laws of Motion>Newton’s Laws of Motion

System shown in the figure is in equilibrium and at rest. The spring and string are massless, now the string is cut. The acceleration of mass

2 m

and

m

just after the string is cut will be
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EASY

Physics>Mechanics>Laws of Motion>Newton’s Laws of Motion

Three blocks A, B and C, of masses

4 kg, 2 kg

1 kg

and respectively, are in contact on a frictionless surface, as shown. If a force of

14 N

is applied on the

4 kg

block, then the contact force between A and B is:

Question Image

MEDIUM

Physics>Mechanics>Laws of Motion>Newton’s Laws of Motion

A mass of

10 kg

is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of

45 °

at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is

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

MEDIUM

Physics>Mechanics>Laws of Motion>Newton’s Laws of Motion

Two masses

m_{1} = 5 kg

and

m_{2} = 10 kg

, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is

0.15

. The minimum weight

m

that should be put on top of

m_{2}

to stop the motion is:

Question Image

MEDIUM

Physics>Mechanics>Laws of Motion>Newton’s Laws of Motion

Two identical springs are connected to mass $m$ as shown $(k = spring constant)$ . If the period of the configuration in (i) is $2 s$ , the period of the configuration (ii) is:

I Question Image

II Question Image

MEDIUM

Physics>Mechanics>Laws of Motion>Newton’s Laws of Motion

One end of a massless spring of spring constant

k

and natural length

l_{0}

is fixed while the other end is connected to a small object of mass

m

lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity

ω

about an axis passing trough fixed end, then the elongation of the spring will be

HARD

Physics>Mechanics>Laws of Motion>Newton’s Laws of Motion

The machine as shown has $2$ rods of length $1 m$ connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has roller that rolls along the floor in a slot. As the roller goes back and forth, a $2 kg$ weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a :

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EASY

Physics>Mechanics>Laws of Motion>Newton’s Laws of Motion

A spring of force constant

k

is cut into lengths of ratio

1 : 2 : 3

. They are connected in series and the new force constant is

k'

. If now they are connected in parallel and force constant is

k''

, then

k' : k''

MEDIUM

Physics>Mechanics>Laws of Motion>Newton’s Laws of Motion

Two blocks

A

and

B

of masses

3 m

and

m

respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of

A

and

B

immediately after the string is cut, are respectively
Question Image

MEDIUM

Physics>Mechanics>Laws of Motion>Newton’s Laws of Motion

A rod of weight

W

is supported by two parallel knife edges

A

and

B

and is in equilibrium in a horizontal position. The knives are at a distance

d

from each other. The centre of mass of the rod is at distance

x

from

A

. the normal reaction on

A

is:

HARD

Physics>Mechanics>Laws of Motion>Newton’s Laws of Motion

On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If r << R, and the surface tension of water is T, value of r just before bubbles detatch is :
(density of water is

ρ_{w}

)

MEDIUM

Physics>Mechanics>Laws of Motion>Newton’s Laws of Motion

A block of mass

10 k g

is in contact against the inner wall of a hollow cylindrical drum of radius

1 m

. The coefficient of friction between the block and the inner wall of the cylinder is

0.1

. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis will be

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

HARD

Physics>Mechanics>Laws of Motion>Newton’s Laws of Motion

A particle of mass

m

is acted upon by a force

F

given by the empirical law

F = \frac{R}{t^{2}} v (t) .

If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot

EASY

Physics>Mechanics>Laws of Motion>Newton’s Laws of Motion

As shown in the figure, an iron block $A$ of volume $0.25 m^{3}$ is attached to a spring $S$ of unstretched length $1.0 m$ and hanging to the ceiling of a roof. The spring gets stretched by $0.2 m$ . This block is removed and another block $B$ of iron of volume $0.75 m^{3}$ is now attached to the same spring and kept on a frictionless incline plane of $30 °$ inclination. The distance of the block from the top along the incline at equilibrium is

Question Image

MEDIUM

Physics>Mechanics>Laws of Motion>Newton’s Laws of Motion

A block of mass $20 kg$ is suspended through two spring balances with negligible mass as shown in figure. What will be the readings in the upper and lower balance respectively ?

Question Image

MEDIUM

Physics>Mechanics>Laws of Motion>Newton’s Laws of Motion

1 kg

block attached to a spring vibrates with a frequency of

1 Hz

on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to a

8 kg

block placed on the same table. So, the frequency of vibration of the

8 kg

block is

The system shown adjacent is in equilibrium. Blocks A,B & C are of equal masses m (Assume springs to be ideal). Then choose the correct statements.

Important Questions on Laws of Motion

Learn and Prepare for any exam you want !

The system shown adjacent is in equilibrium. Blocks $A, B & C$ are of equal masses $m$ (Assume springs to be ideal).

Then choose the correct statements.