Question 1

A projectile is launched at 30° to the horizontal with an initial velocity of 20 m/s. What is the maximum height reached by the projectile? (Take g = 10 m/s²)

Accepted Answer

Maximum height = (u²sin²θ)/(2g) = (400 × sin²30°)/(20) = (400 × 0.25)/20 = 5 m.

Question 2

A stone is thrown horizontally from a cliff with a velocity of 15 m/s. After 2 seconds, what is the vertical component of its velocity? (Take g = 10 m/s²)

Accepted Answer

Vertical velocity at time t: vy = gt = 10 × 2 = 20 m/s (since initial vertical velocity is zero).

Question 3

A projectile has a range of 40 m on level ground when launched at 45°. If the same projectile is launched at 45° with double the initial velocity, what will be its new range?

Accepted Answer

Range is proportional to u²; doubling u makes range 4 times larger: 40 × 4 = 160 m.

Question 4

A particle undergoes uniform circular motion with radius 5 m and completes 2 revolutions in 4 seconds. What is its centripetal acceleration?

Accepted Answer

Angular velocity ω = 2π × (revolutions/time) = 2π × (2/4) = π rad/s; centripetal acceleration = ω²r = π² × 5 = 5π² m/s².

Question 5

A projectile is fired at an angle of 60° with an initial speed of 30 m/s. What is the time of flight? (Take g = 10 m/s²)

Accepted Answer

Time of flight T = (2u sinθ)/g = (2 × 30 × sin60°)/10 = (60 × 0.866)/10 ≈ 5.196 s.

Question 6

A projectile is launched at an angle of 30° with the horizontal from ground level. If the initial velocity is 20 m/s, what is the maximum height reached? (g = 10 m/s²)

Accepted Answer

Maximum height = (v₀ sin θ)²/(2g) = (20 × 0.5)²/(2 × 10) = 100/20 = 5 m.

Question 7

An object undergoes uniform circular motion with a radius of 4 m and completes one full circle in 8 seconds. What is its centripetal acceleration?

Accepted Answer

Centripetal acceleration = ω²r = (2π/T)²r = (2π/8)² × 4 = (π/4)² × 4 = π²/2 m/s².

Question 8

A projectile launched horizontally from a height of 45 m with initial velocity 30 m/s hits the ground. What is the range? (g = 10 m/s²)

Accepted Answer

Time of flight: h = ½gt² → 45 = ½(10)t² → t = 3 s; Range = u₀t = 30 × 3 = 90 m.

Question 9

Two stones are thrown from the same point with the same speed but at angles of 30° and 60° above the horizontal. What is the ratio of their maximum heights?

Accepted Answer

h₁ ∝ sin²(30°) = 1/4 and h₂ ∝ sin²(60°) = 3/4, so h₁:h₂ = 1:3.

Question 10

A particle moves in a circular path of radius 5 m with a constant speed of 10 m/s. What is the period of revolution?

Accepted Answer

Period T = circumference/speed = 2πr/v = 2π(5)/10 = π seconds.

Question 11

A projectile is launched at 45° to the horizontal with initial velocity 20 m/s. What is the range on level ground? (g = 10 m/s²)

Accepted Answer

Range = (v₀² sin 2θ)/g = (400 × sin 90°)/10 = 400/10 = 40 m.

Question 12

In uniform circular motion, which of the following statements is true?

Accepted Answer

In uniform circular motion, the centripetal acceleration is always directed toward the center of the circle, perpendicular to velocity.

Question 13

A ball is thrown at an angle of 60° with initial speed 40 m/s. What is the time of flight? (g = 10 m/s²)

Accepted Answer

Time of flight = (2v₀ sin θ)/g = (2 × 40 × sin 60°)/10 = (80 × √3/2)/10 = 4√3 s.

Question 14

A particle in uniform circular motion has angular velocity ω = 2 rad/s and radius r = 3 m. What is its linear speed?

Accepted Answer

Linear speed v = ωr = 2 × 3 = 6 m/s.

Question 15

A projectile is launched at an angle of 30° to the horizontal with an initial velocity of 40 m/s. Calculate the maximum height reached by the projectile. (Take g = 10 m/s²)

Accepted Answer

Maximum height = (u² sin²θ)/(2g) = (40² × sin²30°)/(2×10) = (1600 × 0.25)/20 = 20 m.

Question 16

A particle moves in a circular path of radius 5 m with a constant speed of 10 m/s. What is the magnitude of centripetal acceleration?

Accepted Answer

Centripetal acceleration = v²/r = (10)²/5 = 100/5 = 20 m/s².

Question 17

A projectile is thrown horizontally from a cliff of height 45 m with an initial velocity of 20 m/s. How far horizontally will it travel before hitting the ground? (Take g = 10 m/s²)

Accepted Answer

Time of flight: h = ½gt² ⟹ t = √(2×45/10) = 3 s; Horizontal range = u×t = 20×3 = 60 m.

Question 18

A particle undergoes uniform circular motion with angular velocity ω = 4 rad/s in a circle of radius 2 m. What is the relationship between linear velocity and centripetal acceleration at any instant?

Accepted Answer

Linear velocity v = ωr = 4×2 = 8 m/s; centripetal acceleration a = ω²r = 16×2 = 32 m/s².

Agniveer (All) Motion in a Plane

Motion in a Plane — Practice Questions