Motion In Two Dimension Test

Result

Motion In Two Dimension Test - 5

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Weekly Quiz Competition

Question 1
4 / -1

A jet airplane travelling from east to west at a speed of 500 km h^-1 ejected out gases of combustion at a speed of 1500 km h^-1 with respect to the jet plane. What is the
velocity of the gases with respect to an observer on the ground?

A
1000 km h^-1 in the direction west to east

B
1000 km h^-1 in the direction east to west

C
2000 km h^-1 in the direction west to east

D
2000 km h^-1 in the direction east to west

Solution
Question 2
4 / -1

A particle is moving along a circular path. The angular velocity, linear velocity, angular acceleration, and centripetal acceleration of the particle at any instant, respectively, are

Which of the following relations is not correct ?

A

B

C

D

Solution

Angular acceleration and angular velocity are along the axis of circular path . So they cannot be perpendicular to each other.
Question 3
4 / -1

A stone is projected from a horizontal plane. It attains maximum height ‘H’ and strikes a stationary smooth wall and falls on the ground vertically below the maximum height. Assuming the collision to be elastic the height of the point on the wall where ball will strike is

A
H/2

B
H/4

C
3H/4

D
None of these

Solution
Question 4
4 / -1

An aircraft moving with a speed of 972 km/h is at a height of 6000 m, just overhead of an anti-aircraft gun. If the muzzle velocity of the gun is 540 m/s, the firing angle θ for the bullet to hit the aircraft should be

A
73^o

B
30^o

C
60^o

D
45^o

Solution

Displacement of aircraft in time t = horizontal displacement of projectile
Question 5
4 / -1

An aeroplane is to go along straight line from A to B, and back again. The relative speed with respect to wind is V. The wind blows perpendicular to line AB with speed v The distance between A and B is l The total time for the round trip is

A

B

C

D

Solution
Question 6
4 / -1

Two cars of masses m₁ and m₂ are moving in circles of radii r₁ and r₂ respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is :

A
m₁r₁ : m₂r₂

B
m₁ : m₂

C
r₁: r₂

D
1 : 1

Solution

Since both make complete circles in same time 't'. so angular velocity is also same for both the masses.

since centripetal acceleration a = ω²r
Question 7
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 8
4 / -1

A particle is moving on a circular path of radius r with uniform speed V. The magnitude of change in velocity when the particle moves from P to Q is :- (∠PPOQ=40^o)

A
2v cos40^o

B
2v sin40^o

C
2v sin20^o

D
2v cos20^o

Solution

Let the velocity at point P
Question 9
4 / -1

A particle is projected from the ground with an initial speed of v at an angle θ with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is?

A

B

C

D
v cos θ

Solution

For highest point-
Question 10
4 / -1

A helicopter is flying horizontally at 8 m/s at an altitude 180 m when a package of emergency medical supplies is ejected horizontally backward with a speed of 12 m/s relative to the helicopter. Ignoring air resistance, what is the horizontal distance between the package and the helicopter when the package hits the ground?

A
120 m

B
24 m

C
36 m

D
72 m

Solution

Time taken by packet to reach the ground:

Horizontal distance travelled by helicopter in this time

= 8 x 6 = 48 m.

Velocity of package w.r.t. ground

= 12 - 8 = 4 m/s in backward direction.

Horizontal distance travelled by package in time,

T=4 x 6=24m.

So, horizontal distance between them = 48 + 24 = 72 m