NCERT Class 11 Physics Solutions: Chapter 4 – Motion in a Plane Part 7

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Question 4.16:

A cricketer can throw a ball to a maximum horizontal distance of 100 m. How much high above the ground can the cricketer throw the same ball?

Answer:

Maximum horizontal distance = R

The cricketer will only be able to throw the ball to the maximum horizontal distance, when the angle of projection is 45°.

i.e., θ = 45°.

The relation gives the horizontal range for a projection velocity v:

The ball will achieve the maximum height when it is thrown vertically upward. For such motion, the final velocity v is zero at the maximum height H.

Acceleration, a = – g

Using the third equation of motion:

Question 4.17:

A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude and direction of acceleration of the stone?

Answer:

Length of the string,

Number of revolutions = 14

Time taken = 25 s

Frequency,

Angular frequency, ω = 2πν

Centripetal acceleration,

The direction of centripetal acceleration is always directed along the string, toward the centre, at all points.

Question 4.18

An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900 km/h. Compare its centripetal acceleration with the acceleration due to gravity.

Answer:

Radius of the loop, r = 1 km = 1000 m

Speed of the aircraft,

Centripetal acceleration,

Acceleration due to gravity, g = 9.8

Question 4.19:

Read below each statement carefully and state, with reasons, if it is true or false:

(a) The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre

(b) The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point

(c) The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector

Answer:

(a) The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre : False

Explanation:

The net acceleration of a particle in circular motion is not always directed along the radius of the circle toward the centre. It happens only in the case of uniform circular motion.

(b) The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point : True

Explanation:

At a point on a circular path, a particle appears to move tangentially to the circular path. Hence, the velocity vector of the particle is always along the tangent at a point.

(c) The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector: True

Explanation:

In uniform circular motion (UCM), the direction of the acceleration vector points toward the centre of the circle. However, it constantly changes with time. The average of these vectors over one cycle is a null vector.