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

EASY

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A metal sphere is hung by a string fixed to a wall. The forces acting on the sphere are shown in figure. Which of the following statements is/are correct?

a. $\vec{N} + \vec{T} + \vec{W} = 0$

b. $T^{2} = N^{2} + W^{2}$

c. $T = N + W$

d. $N = W \tan θ$

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Important Questions on Laws of Motion

MEDIUM

Physics>Mechanics>Laws of Motion>Equilibrium of a Particle

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>Equilibrium of a Particle

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>Equilibrium of a Particle

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>Equilibrium of a Particle

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>Equilibrium of a Particle

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>Equilibrium of a Particle

Pick out the correct statement

HARD

Physics>Mechanics>Laws of Motion>Equilibrium of a Particle

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>Equilibrium of a Particle

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>Equilibrium of a Particle

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>Equilibrium of a Particle

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>Equilibrium of a Particle

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>Equilibrium of a Particle

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>Equilibrium of a Particle

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>Equilibrium of a Particle

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>Equilibrium of a Particle

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>Equilibrium of a Particle

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>Equilibrium of a Particle

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>Equilibrium of a Particle

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>Equilibrium of a Particle

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>Equilibrium of a Particle

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})

A metal sphere is hung by a string fixed to a wall. The forces acting on the sphere are shown in figure. Which of the following statements is/are correct? a. N→+T→+W→=0 b. T2=N2+W2 c. T=N+W d. N=Wtan⁡θ

Important Questions on Laws of Motion

Learn and Prepare for any exam you want !

A metal sphere is hung by a string fixed to a wall. The forces acting on the sphere are shown in figure. Which of the following statements is/are correct?

a. $\vec{N} + \vec{T} + \vec{W} = 0$

b. $T^{2} = N^{2} + W^{2}$

c. $T = N + W$

d. $N = W \tan θ$