CBSE Class 11 Motion in Plane Worksheet A

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Question. The component of vector a̅ = 2î + 3ĵ along the vector î + ĵ is
(a) 5/√2
(b) 10 √2
(c) 5 √2
(d) 5

Answer: A

Question. A particle moves so that its position vector is given by r̅ = cosωtx̅ + sinωty̅. Where ω is a constant. Which of the following is true ?
(a) Velocity and acceleration both are perpendicular to r̅
(b) Velocity and acceleration both are parallel to r̅
(c) Velocity is perpendicular to r̅ and acceleration is directed towards the origin
(d) Velocity is perpendicular to r̅ and acceleration is directed away from the origin

Answer: C

Question. A body is projected at an angle of 30º to the horizontal with speed 30 m/s. What is the angle with the horizontal after 1.5 seconds? Take g = 10 m/s².
(a) 0º
(b) 30º
(c) 60º
(d) 90º

Answer: A

Question. A projectile is moving at 60 m/s at its highest point, where it breaks into two equal parts due to an internal explosion.
One part moves vertically up at 50 m/s with respect to the ground. The other part will move at a speed of
(a) 110 m/s
(b) 120 m/s
(c) 130 m/s
(d) 10 √61 m/ s

Answer: C

Question. A particle having a mass 0.5 kg is projected under gravity with a speed of 98 m/sec at an angle of 60º. The magnitude of the change in momentum (in N-sec) of the particle after 10 seconds is
(a) 0.5
(b) 49
(c) 98
(d) 490

Answer: B

Question. A large number of bullets are fired in all directions with the same speed v. What is the maximum area on the ground on which these bullets will spread?
(a) πV²/g
(b) πV⁴/g²
(c) π² v²/g²
(d) π²V⁴/g²

Answer: B

Question. If |a̅ + b̅| = a̅ - b̅| then angle between a̅ & b̅ is
(a) 45º
(b) 30º
(c) 90º
(d) 180º

Answer: C

Question. Two bullets are fired horizontally, simultaneously and with different velocities from the same place. Which bullet will hit the ground earlier ?
(a) It would depend upon the weights of the bullets.
(b) The slower one.
(c) The faster one.
(d) Both will reach simultaneously.

Answer: D

Question. A cricket ball is hit with a velocity 25 ms^-1 , 60° above the horizontal. How far above the ground, ball passes over a fielder 50 m from the bat (consider the ball is struck very close to the ground)?
Take √3 =1.7 and g = 10 ms^–2
(a) 6.8 m
(b) 7 m
(c) 5 m
(d) 10 m

Answer: C

Question. The angles which the vector A̅ = 3î + 6ĵ + 2k̂ makes with the co-ordinate axes are : 

Answer: B

Question. The resultant of two forces 3P and 2P is R. If the first force is doubled then the resultant is also doubled. The angle between the two forces is
(a) 60º
(b) 120º
(c) 70º
(d) 180º

Answer: B

Question. The equation of a projectile is y = √3x - gx²/2 The angle of projection is given by
(a) tanθ = 1/√3
(b) tanθ = √3
(c) π/2
(d) zero.

Answer: B

Question. A body is thrown horizontally with a velocity √2gh from the top of a tower of height h. It strikes the level ground through the foot of the tower at a distance x from the tower.
The value of x is
(a) gh
(b) gh/2
(c) 2h
(d) 2gh/3

Answer: C

Question. A plane flying horizontally at a height of 1500 m with a velocity of 200 ms^–1 passes directly overhead on antiaircraft gun. Then the angle with the horizontal at which the gun should be fired from the shell with a muzzle velocity of 400 ms^–1 to hit the plane, is
(a) 90°
(b) 60°
(c) 30°
(d) 45°

Answer: B

Question. A projectile A is thrown at an angle of 30° to the horizontal from point P. At the same time, another projectile B is thrown with velocity v₂ upwards from the point Q vertically below the highest point. For B to collide with A,v₁/v₂ should be (51)
(a) 1
(b) 2
(c) 1/2
(d) 4 

Answer: C

Question. If the sum of two unit vectors is a unit vector, then the magnitude of their difference is
(a) √3
(b) √2
(c) √5
(d) 1/√2

Answer: A

Question. In a two dimensional motion, instantaneous speed v₀ is a positive constant. Then, which of the following are necessarily true?
(a) The acceleration of the particle is zero
(b) The acceleration of the particle is bounded
(c) The acceleration of the particle is necessarily in the plane of motion
(d) The particle must be undergoing a uniform circular motion 

Answer: C

Question. A body of 3kg. moves in X-Y plane under the action of force given by 6tî + 4tĵ . Assuming that the body is at rest at time t = 0, the velocity of body at t = 3 sec is
(a) 9î + 6ĵ
(b) 18î + 6ĵ
(c) 18î + 12ĵ
(d) 12î + 68ĵ

Answer: A

Question. A bullet is fired with a speed of 1500 m/s in order to hit a target 100 m away. If g = 10 m/s2. The gun should be aimed
(a) 15 cm above the target
(b) 10 cm above the target
(c) 2.2 cm above the target
(d) directly towards the target

Answer: C

Question. A projectile of mass m is thrown with a velocity v making an angle 60° with the horizontal. Neglecting air resistance, the change in momentum from the departure A to its arrival at B, along the vertical direction is
(a) 2 mv
(b) √3mv
(c) mv
(d) mv/√3

Answer: B

Question. A person sitting in the rear end of the compartment throws a ball towards the front end. The ball follows a parabolic path. The train is moving with velocity of 20 m/s. A person standing outside on the ground also observes the ball. How will the maximum heights (ym) attained and the ranges (R) seen by the thrower and the outside observer compare with each other?
(a) Same y_m different R
(b) Same y_m and R
(c) Different y_m same R
(d) Different ym and R

Answer: A

Question. A force of (3î + 4ĵ) N acts on a body and displaces it by (3î + 4ĵ) m. The work done by the force is
(a) 5 J
(b) 30 J
(c) 25 J
(d) 10 J

Answer: C

Question. The position vector of a particle R̅ as a function of time is given by:
R̅ = 4sin(2πt) î+4cos(2πt)ĵ 
Where R is in meter, t in seconds and î and ĵ denote unit vectors along x-and y-directions, respectively.
Which one of the following statements is wrong for the motion of particle?
(a) Magnitude of acceleration vector is v2/R, where v is the velocity of particle
(b) Magnitude of the velocity of particle is 8 meter/second
(c) path of the particle is a circle of radius 4 meter.
(d) Acceleration vector is along -R̅

Answer: B

Question. A cyclist moving at a speed of 20 m/s takes a turn, if he doubles his speed then chance of overturn
(a) is doubled
(b) is halved
(c) becomes four times
(d) becomes 1/4 times

Answer: D

Question. A person swims in a river aiming to reach exactly on the opposite point on the bank of a river. His speed of swimming is 0.5 m/s at an angle of 120º with the direction of flow of water. The speed of water is
(a) 1.0 m/s
(b) 0.5 m/s
(c) 0.25 m/s
(d) 0.43 m/s

Answer: C

Question. A gun is aimed at a horizontal target. It takes 1/2 s for the bullet to reach the target. The bullet hits the target x metre below the aim. Then, x is equal to
(a) 9.8/4 m
(b) 9.8/8 m
(c) 9.8 m
(d) 19.6 m.

Answer: B

Question. If a̅ = î - ĵ + k̂and b̅ 2î + ĵ + 3k̂, then the unit vector along a̅ + b̅ is
(a) 3i + 4k/5
(b) -3i + 4k/5
(c) -3i - 4k/5
(d) None of these

Answer: A

Question. The position vector of a particle is r̅ = (a cos ωt) î + (a sin ωt)ĵ . The velocity of the particle is
(a) directed towards the origin
(b) directed away from the origin
(c) parallel to the position vector
(d) perpendicular to the position vector

Answer: D

1. What is “Trajectory of a projectile?

2. A projectile is fired at an angle of 30° with the horizontal with velocity 10m/s. At what angle with the vertical should it be fired to get maximum range?

3. What is the value of angular speed for 1 revolution?

4. What is the angle between two forces of 2N and 3N having resultant as 4N?

5. What is the angle of projection at which horizontal range and maximum height are equal?

6. Prove that for elevations which exceed or fall short of 45° by equal amounts the ranges are equal?

7. At what range will a radar set show a fighter plane flying at 3 km above its centre and at distance of 4 km from it?

8. Derive expressions for velocity and acceleration for uniform circular motion.

OR

Derive expression for linear acceleration in uniform circular motion.

9. Derive an equation for the path of a projectile fired parallel to horizontal.

10. (a) Define time of flight and horizontal range?

(b) From a certain height above the ground a stone A is dropped gently. 

Simultaneously another stone B is fired horizontally. Which of the two stones will arrive on the ground earlier? 

Click on link below to download CBSE Class 11 Motion in Plane Worksheet A.