## Kerala Plus One Physics Chapter Wise Questions and Answers Chapter 4 Motion in a Plane

**Very Short Answer Type Questions (Score 1)**

Question 1.

Given that and P + Q = R, where P, Q and R are the magnitude of vectors respectively. The angle between is ……………….

Answer:

0 (both are in the same direction)

Question 2.

In the motion of a rocket, physical quantity which is conserved is ……………..

Answer:

a. Angular momentum

b. Linear momentum

c. Work

d. Force

Answer:

Linear momentum

Question 3.

Given that and

The angle between is

Answer:

c. π/2 ( is perpendicular to )

Question 4.

The resultant of two vectors has minimum magnitude. When the angle between them is

a. 0°

b. 45°

c. 90°

d. 180°

Answer:

d. 180° (in opposite direction)

Question 5.

Which of the following doesn’t affect the maximum height attained by the projectile?

a. Magnitude of initial velocity

b. Acceleration of the projectile

c. Angle of projection

d. Mass of the projectile

Answer:

d. Mass of the projectile

Question 6.

“A projectile has maximum value for time of flight when angle of projection is 45°”. State whether this statement is true or false.

Answer:

False.

T is maximum when 0 = 90°

Question 7.

The relative velocity of a particle moving with a velocity V, with respect to itself is

a. zero

b. V

c. -V

d. 2V

Answer:

a. zero

Question 8.

Two bullets are fired horizontally with different velocities from the same heights. Which will reach the ground first ?

a. slower one

b. faster one

c. both reach simultaneously

d. it cannot be predicted

Answer:

c. downward acceleration and velocity is same for both, so both will reach simultaneously.

Question 9.

The rectangular components of a force 5 N in the following set is

a. 1 N, 4 N

b. 2 N, 3 N

c. 4 N, 3 N

d. 2.5 N, 2.5 N

Answer:

c. 4 N, 3 N

Question 10.

Two forces 4 N and 3 N are acting perpendicular to each other. The magnitude of the resultant is

a. 7 N

b. 5 N

c. 1 N

d. 25 N

Answer:

b.5 N

**Short Answer Type Questions (Score 2)**

Question 1.

a. The path of a projectile is a

b. The method for the addition of vectors is known as

Answer:

a. parabola

b. parallelogram method

Question 2.

a. Two bodies are moving in opposite direction with velocity V. The relative velocity of one with respect to other is

a. zero

b. V

c. V/2

d. 2V

b. The two particle moving with velocities v_{1} and v_{2}. Their relative velocity is maxi-mum when the angle between their Velocities is …………..

a. 0

b. kI4

c.π/2

d. π

Answer:

a. d.Relative velocity = V-(-V) = 2V

b. d.π (particles moves in opposite direction)

Question 3.

Match the Following:

Answer:

Question 4.

Two trains A and B are moving on parallel tracks with velocities 100 km/h and 150 km/h respectively directed in the same direction.

i. What is the relative velocity of A with respect to B?

ii.What is the relative velocity of B with respect to A?

Answer:

i. V_{AB}– V_{A} – V_{B}= 100 – 150 = -50 km/h

ii. V_{BA}– V_{B} – V_{A}

Question 5.

a. Define scalar quantity with examples

b. Define vector quantity with examples

Answer:

a. Scalar quantities are quantities with magnitudes only. eg., distance, speed, mass and temperature.

b. Vector quantities are quantities with magnitude and direction both, eg., displacement, velocity and acceleration.

**Short Answer Type Questions (Score 3)**

Question 1.

In figure, two vectors are acting at an angle θ as shown

a. Complete the diagram to show the magnitude and direction of the resultant of the two vectors.

b. Find the magnitude of the vectors and angle 6 between them.

Answer:

Question 2.

A body is projected vertically upwards with a velocity u, it reaches the maximum height and comes back to the same point.

a. What is the velocity of the body at the maximum height?

b. Draw the velocity-time graph and speed-time graph of the body

Answer:

a. At maximum height velocity becomes ‘Zero’

Question 3.

The figure below shows a particle executing uniform circular motion. , are the velocities of the particle at two different positions P and Q

a. Define uniform circular motion.

b. Choose the correct entries from the bracket.

i. is (equal /not equal) to

ii. The particle has (same / different) direction for velocities at P.

iii. The acceleration of the particle is (zero/ non zero) directed towards centre.

iv. The angular speed ω , of the particle is (constant / non constant).

Answer:

a. When an object follows a circular path at constant speed, the motion of the object is called uniform circular motion,

b. i. equal

ii. different

iii. non-zero

iv. constant

Question 4.

Two particles A and B starts from 0 at the same time and moves along straight lines OA and OB respectively. If the particles have the uniform velocities such that =v and α=β=45º

i. What is the angle between

ii. Find the relative velocity of B with respect to A.

Answer:

Question 5.

A boy pulls a rope attached to a stone with a force of 40 N. The rope makes an angle 30° with the horizontal.

a. Calculate the pulling force which tends to move the stone along the ground.

b. Calculate the force tending to lift the stone above the ground

Answer:

a. 40 cos 30° = 40×

b.40 sin 30° = 20 N

**Long Answer Type Questions (Score 4)**

Question 1.

A cricket ball is thrown at an angle 6 above the horizontal. The motion of the cricket ball is an example of projectile motion.

i. What is a projectile?

ii. If the projectile is launched with an initial velocity V_{o}, the horizontal and vertical components of velocity are

iii. Which components of velocity remains constant throughout the motion?

iv. If the other components changes, what is the acceleration produced when the projectile moves up?

Answer:

i. An object that is in flight.

ii. V_{o} cos θ, V_{o} sin θ respectively

iii.Horizontal

iv. -g

Question 2.

A frog sees an insect at a horizontal distance of 1 m from it. The frog can jump with a maximum speed of 4 m/s in any direction. The frog jumps with its maximum initial speed and lands on the insect.

a. What is the type of motion made by the frog?

b. Find the angle that the frog’s initial velocity made with horizontal.

c. Find the minimum distance that the insect has to keep the frog so that it can escape from the frog.

Answer:

Question 3.

A uniform solid cube has a mass of 3 kg and its volume is 10^{-3} m^{3}.

i. Choose the correct entries in the bracket.

a. Mass is a (vector / scalar) quantity.

b. Volume is a (vector/scalar) quantity.

ii. Find density (density =mass/volume), state if it is a scalar or vector quantity.

iii. State the rule for algebraic operation with scalars.

Answer:

i. a. Scalar

b. Scalar

ii. 3 × 10^{3} kg/m^{3}, scalar quantity.

iii. Scalars can be treated just like ordinary numbers.

Question 4.

What should be the angle of projection, so that the horizontal range is equal to the maximum height ?

a. tan^{-1} 1

b. tan^{-1} 2

c. tan^{-1} 3

d. tan^{-1} 4

Answer:

**Very Long Answer Type Questions (Score 5)**

Question 1.

A boy throws a cricket bail with velocity u at an angle 0 with the horizontal

a. Draw the path followed by the ball.

b. Derive an expression for the maximum height reached by the ball,

a. If the ball is thrown with a velocity of 28 ms^{1} in a direction 300 with the horizontal, find the time taken by the ball to return to the same horizontal level.

Answer:

Question 2.

The position P of a particle in X, Y reference frame is given below.

i. If are unit vectors along X and Y, represent in terms of .

ii. Find |Qp|.

iii. Magnitude of a vector is a scalar. State if it is true or false.

iv. What is the magnitude of

a. unit vector

b. zero vector

v. Define resolution of vectors. What are the components of in X and Y direction?

Answer:

iii. True

iv. a.1 b.0

v. Splitting up of a single vector into two or more component vrctor ,4 and 3.

Question 3.

A projectile is projected with a velocity of . The range of the projectile is twice its maximum height.

a. Prove that tan θ = 2.

b. Calculate the angle if projection, if the maximum range of a projectile is times the acual range.

c. Prove that there are two angles of projection for the same horizontal range.

Answer:

Hence there are two angles ‘θ_{0}’ and ‘(90°-θ_{0})’ for a projectile with the same range for the same initial velocity.

Question 4.

The figure shows the displacement of a boy moving on a ground, starting from the centre.

a. What is the displacement of the body towards east and towards north?

b. What is the magnitude of the resultant displacement ?

c. At the position ‘B’, the boy climbs up through a post 6m. What is the total displacement of the boy?

Answer:

**NCERT Questions and Answers**

Question 1.

Given below are some physical quantities: speed, acceleration, velocity, density, displacement, no. of moles, work, force, momentum and current.

i. What is a scalar quantity?

ii. Define a vector quantity?

iii. Classify the above quantities into vectors and scalars.

Answer:

i. Scalar quantities are quantities with magnitudes only. eg., distance, speed, mass and temperature.

ii. Vector quantities are quantities with magnitude and direction both, eg., displacement, velocity and acceleration.

iii. Scalars- Speed, density, number of moles, work, current.

Vectors- Acceleration, velocity, displacement, force, momentum.

Question 2.

A man can swim with a speed at 4 km/h in the still water. He tries to cross a river which flows steadily at 3 km/h. Assume that the man swim perpendicular to the bank of the river. Make use of the graphical representation given below:

V_{m} = velocity of the man

V_{r} = velocity of the river water

i. Using a vector addition, find the resultant velocity of the man.

ii. The swimmer tries to swim perpendicular to the river bank, but he is deviated by the flowing water. Write necessary steps to calculate the deviation of the swimmer:

[Hint: Angle between V_{m} and resultant velocity]

iii. If river is 1 km wide, how long does he take to cross the river.

Answer:

Question 3.

The position of a particle is given by,

i. Find the velocity of the particle.[Hint:

ii. Write the components of velocity in x, y and z direction.

iii. Estimate magnitude of velocity at t = 2s.

Answers:

Question 4.

A particle starts from the origin at t = Os with the velocity of m/s and moves in the xy plane with a constant acceleration of

. At t = 2s calculate the following:

i. Displacement

ii. Velocity

iii. Speed

Answer:

Question 5.

A cricketer can throw a ball to a maximum horizontal distance of 100 m.

a. What is the expression for horizontal range of a projectile?

b. What is the value of 0 so that the horizontal range is the maximum?

c. Find the maximum velocity with which cricketer can throw the bail.

d. How much high above the ground can cricketer throw the ball?

Answer:

Question 6.

A stone tied to the end of a string 80 cm long is whirled in horizontal circle with a constant speed. The stone makes 14 revolutions in 25 seconds.

a. What is the total angle in radians described by the stone in 25 seconds?

b. Find the angular speed of the stone.

c. Find the speed of the stone.

d. Estimate the magnitude of the acceleration of the stone. What is the direction of acceleration?

Answer:

a.Total angle = 2k × 14 radians

b. Angular speed to = 2πn = 2×3.14×14/25

= 3.52 rad/s

where n = frequency

c. V = rω = 0.8 ×3.52 = 2.8 m/s

d. a = V^{2}/r = rω^{2} = 0.8 × (3.52)^{2} = 9.8 m/s^{2 }The acceleration is directed towards the centre.

Question 7.

In a harbour, wind is blowing at the speed of 72 km/h and the flag on the mast of a boat anchored in the harbour flutters along the N-E direction. If the boat starts moving at a speed of 51 km/h to the north, what is the direction of the flag on the mast of the boat ?

Answer:

East.

Question 8.

On an open ground, a motorist follows a track that turns to his left by an angle of 60° after every 500 m. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.

Answer:

Displacement of magnitude 1 km and direction 60° with the initial direction. Total path length=1.5 km (third turn).

Magnitude of displacement = 1000 m Path length = 3 km (sixth turn)

Null displacement vector.

Path length=4 km (eighth turn).

Displacement vector = 866 m, 30°

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