Motion In Two Dimension Test

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Motion In Two Dimension Test - 3

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Question 1
4 / -1

A particle is projected from point O with velocity u in a direction making an angle α with the horizontal. At any instant its position is at point p at right angles to the initial direction of projection, Its velocity at point p is:

A
u tan α

B
u cot α

C
u sec α

D
u cosec α

Solution

Horizontal velocity at point O = u cos α
Horizontal velocity at point P = v sin α
In projectile motion horizontal, component of velocity remains constant throughout the motion
∴ v sin α = u cos α
⇒ v = u cot α
Question 2
4 / -1

Pankaj and Sudhir are playing with two different balls of masses m and 2m, respectively. If Pankaj throws his ball vertically up and Sudhir at an angle θ, both of them stay in our view for the same period. The height attained by the two balls are in the ratio:

A
2 : 1

B
1 : 1

C
1 : cos θ

D
1 : sec θ

Solution

Time of flight for the ball thrown by pankaj,
Time of flight for the ball thrown by sudhir,According to problem,

Height of the ball thrown by pankaj,
Height of the thrown by sudhir,
Question 3
4 / -1

A ship A sailing due east with a velocity of 10 km/h happens to appear sailing due north with a velocity of 5 km/h, to a person, sitting in a moving ship B. Determine the velocity (absolute) of ship B.
.

A

B
5√5 km/h, tan⁻¹(1/2) E of S

C
4√5 km/h, tan⁻¹(1/2) S of E

D
4√5 km/h, tan⁻¹(1/2) E of S

Solution

Here we are given velocity of 'A',
Velocity of 'A', w.r.t. 'B',
Now,

Hence velocity of B,
i.e. S of E
Question 4
4 / -1

A boy projects a stone vertically perpendicular to the trolley car with a speed v. If the trolley car moves with u constant velocity m, the time of flight of the stone is:

A

B

C

D
None of These

Solution

v = v₀sin θ
u = v₀cos θ
Time of flight depends on vertical component of velocity.
Question 5
4 / -1

Which of the following statements is false for a particle moving in a circle with a constant angular speed?

A
The acceleration vector points to the centre of the circle.

B
The acceleration vector is tangent to the circle.

C
The velocity vector is tangent to the circle.

D
The velocity and acceleration vectors are perpendiculai to each other.

Solution

In circular motion we know the velocity vector is tangent to the circle. If a particle moves in a circle with constant angular speed it perform uniform circular motion. In uniform circular motion the tangential acceleration of the particle is zero. The particle moves under radial acceleration only which points to the centre of the circle. Hence the velocity and acceleration vectors are perpendicular to each other.
Question 6
4 / -1

A particle is moving on a circular path of radius r with uniform velocity v. The change in velocity when the particle moves from P to Q is (∠POQ=40^∘).

A
2v cos 40^∘

B
2v sin 40^∘

C
2v cos 20^∘

D
2v sin 20^∘

Solution

Change in velocity:
Question 7
4 / -1

A stone is just released from the window of a train moving along a horizontal straight track. The stone will hit the ground following.

A
Straight path

B
Circular path

C
Parabolic path

D
Hyperbolic path

Solution

Due to constant velocity along horizontal and vertical downward force of gravity stone will hit the ground following parabolic path.
Question 8
4 / -1

An aeroplane is flying horizontally with a velocity of 600 km/h at a height of 1960 m. When it is vertically at a point A on the ground, a bomb is released from it. The bomb strikes the ground at point B. The distance AB is:

A
1200 m

B
0.33 km

C
3.33 km

D
33 km

Solution

Horizontal displacement of the bomb AB = Horizontal velocity × time available
Question 9
4 / -1

A particle is dropped from a height and another particle is thrown in horizontal direction with speed of 5 m/sec from the same height. The correct statement is:

A
Both particles will reach at ground simultaneously.

B
Both particles will reach at ground with same speed.

C
Particle will reach at ground first with respect to particle.

D
None of these

Solution

For both cases,
Because vertical downward component of velocity will be zero for both the particles.
Question 10
4 / -1

A projectile fired with initial velocity u at some angle θ has a range R. If the initial velocity be doubled at the same angle of projection, then the range will be:

A
2R

B
R/2

C
R

D
4R

Solution

If initial velocity be doubled then range will become four times.
Question 11
4 / -1

The radius vector describing the position of the particle A relative to origin.

Find the rectangular components of the average velocity in the time interval between t and t + Δ t.

A
(Δ t + 2t), (Δ t + 2t - 2)

B
(Δ t - 2t), (Δ t + 2t - 2)

C
(Δ t - t), (Δ t + 2t + 2)

D
(Δ t + t), (Δ t + 2t )

Solution