A particle moving in the xy -plane experiences a velocity dependent force F → = k υ y i ^ + υ x j ^ , where υ x and υ y are the x and y components of its velocity υ → . If a → is the acceleration of the particle, then which of the following statements is true for the particle ?

quantity υ → × a → is constant in time

F → arises due to a magnetic field

kinetic energy of particle is constant in time

quantity υ → . a → is constant in time

HARD

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A block of mass $M$ slides on a frictionless surface with an initial speed of $v_{0}$ . On top of the block is a small box of mass $m$ . The coefficients of friction between box and block are $μ_{s}$ and $μ_{k}$ . The sliding block encounters an ideal spring with a force constant $k$ . Answer the following questions.

Suppose the value of $k$ is just slightly greater than the value found in the previous question, so that the box begins to slide just as the spring reaches maximum compression.

The accelerations of box and block are, respectively.

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Important Questions on Laws of Motion

MEDIUM

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A mass of

10 k g

is suspended by a rope of length

4 m

, from the ceiling. A force

F

is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of

45 °

with the vertical. Then

F

equals: (Take

g = 10 m s^{- 2}

and the rope to be massless)

HARD

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A block of weight

100 N

is suspended by copper and steel wires of same cross-sectional area

0.5 c m^{2}

and, length

\sqrt{3} m

and

1 m,

respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copper and steel wires with ceiling are

30^{o}

and

60^{o},

respectively. If elongation in copper wire is

(Δ l_{C})

and elongation in steel wire is

(Δ l_{S}),

then the ratio

\frac{Δ l_{C}}{Δ l_{S}}

\frac{x}{1}

.Find the value of

x

.
[Young's modulus for copper and steel are

1 \times 10^{11} N m^{- 2}

and

2 \times 10^{11} {Nm}^{- 2}

respectively]

Question Image

HARD

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

60 H P

electric motor lifts an elevator having a maximum total load capacity of

2000 k g .

If the frictional force on the elevator is

4000 N,

the speed of the elevator at full load is close to :

(1 HP = 746 W, g = 10 m s^{- 2})

EASY

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A force of

(2 \hat{i} + 3 \hat{j}) N

acts on a body of mass

1 kg

which is at rest initially. The acceleration of the body is

HARD

Physics>Mechanics>Laws of Motion>Newton's Second Law 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}

)

EASY

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

Pick out the correct statement

HARD

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A ball is thrown upward with an initial velocity

V_{0}

from the surface of the earth. The motion of the ball is affected by a drag force equal to

m γ v^{2}

(where

m

is mass of the ball,

v

is its instantaneous velocity and

γ

is a constant). Time taken by the ball to rise to its zenith is:

MEDIUM

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A particle moving in the

xy

-plane experiences a velocity dependent force

\vec{F} = k (υ_{y} \hat{i} + υ_{x} \hat{j})

, where

υ_{x}

and

υ_{y}

are the

x

and

y

components of its velocity

\vec{υ}

. If

\vec{a}

is the acceleration of the particle, then which of the following statements is true for the particle ?

MEDIUM

Physics>Mechanics>Laws of Motion>Newton's Second Law 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 Second Law 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})

MEDIUM

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A body of mass

2 kg

is moving with a momentum of

10 kg {ms}^{- 1} .

The force needed to increase its kinetic energy by four times in

10

seconds is

MEDIUM

Physics>Mechanics>Laws of Motion>Newton's Second Law 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 Second Law of Motion

A machine gun has a mass

5 kg

. It fires

50

gram bullets at the rate of

30

bullets per minute at a speed of

400 m s^{- 1} .

What force is required to keep the gun in position?

HARD

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

An elevator in a building can carry a maximum of

10

persons, with the average mass of each person being

68 k g

. The mass of the elevator itself is

920 k g

and it moves with a constant speed of

3 m / s

. The frictional force opposing the motion is

6000 N

. If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator

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

must be at least:

MEDIUM

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A block starts moving up an inclined plane of inclination

30 °

with an initial velocity of

v_{0}

. It comes back to its initial position with velocity

\frac{v_{0}}{2} .

The value of the coefficient of kinetic friction between the block and the inclined plane is close to

\frac{1}{1000},

The nearest integer to

I

is :

HARD

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A body of mass

m

is moving in a straight line with momentum

p

. Starting at time

t = 0

, a force

F = a t

acts in the same direction on the moving particle during time interval of

T

. So that its momentum changes from

p

2 p

. The value of

T

EASY

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A block $A$ of mass $100 kg$ rests on another block $B$ of mass $200 kg$ and is tied to a wall as shown in the figure. The coefficient of friction between $A$ and $B$ is $0.2$ and that between $B$ and ground is $0.3$ . The minimum force required to move the block $B$ is $(g = 10 m s^{- 2})$

Question Image

EASY

Physics>Mechanics>Laws of Motion>Newton's Second Law of Motion

A particle moving with velocity $\vec{V}$ is acted by three forces shown by the vector triangle $P Q R$ . The velocity of the particle will
Question Image

MEDIUM

Physics>Mechanics>Laws of Motion>Newton's Second Law 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:

MEDIUM

Physics>Mechanics>Laws of Motion>Newton's Second Law 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})

Important Questions on Laws of Motion

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