Mechanics Study Materials for Competitive Exam Prep

Mechanics

Conservation of Momentum Current Electricity (Advanced) Dynamics of Rigid Bodies Electromagnetic Induction Electrostatics (Advanced) Friction and Circular Motion Gravitation Impulse and Momentum Problems Kinematics: Motion in One Dimension Kinematics: Motion in Two Dimensions (Projectile Motion) Kinetic Theory of Gases Laws of Motion Magnetism & Matter Newtons Laws of Motion Nuclei & Atoms - Advanced Optics - Ray and Wave Properties of Matter Relative Motion Concepts Rolling Motion and Stability Rotational Kinematics and Dynamics Simple Harmonic Motion System of Particles Thermodynamics (Advanced) Units and Measurements Work, Energy and Power

Q. A 0.5 kg soccer ball is kicked, resulting in a change in velocity from 0 m/s to 10 m/s. What is the impulse given to the ball?

A. 5 Ns
B. 10 Ns
C. 2.5 Ns
D. 1 Ns

Solution

Impulse (J) = mass (m) × change in velocity (Δv) = 0.5 kg × (10 m/s - 0 m/s) = 5 Ns.

Correct Answer: A — 5 Ns

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Q. A 1 kg object moving at 5 m/s collides with a stationary object. If the collision is perfectly elastic, what is the final momentum of the system?

A. 5 kg·m/s
B. 0 kg·m/s
C. 10 kg·m/s
D. 2.5 kg·m/s

Solution

In a perfectly elastic collision, momentum is conserved. Initial momentum = 1 kg × 5 m/s = 5 kg·m/s.

Correct Answer: A — 5 kg·m/s

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Q. A 10 kg object is dropped from a height of 20 m. What is its speed just before it hits the ground? (Assume no air resistance)

A. 10 m/s
B. 14 m/s
C. 20 m/s
D. 28 m/s

Solution

Using conservation of energy: Potential Energy = Kinetic Energy. mgh = 0.5mv². v = sqrt(2gh) = sqrt(2 × 9.8 m/s² × 20 m) = 20 m/s.

Correct Answer: C — 20 m/s

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Q. A 15 kg box is pushed with a force of 30 N. What is the box's acceleration?

A. 1 m/s²
B. 2 m/s²
C. 3 m/s²
D. 4 m/s²

Solution

Using F = ma, we find acceleration: a = F/m = 30 N / 15 kg = 2 m/s².

Correct Answer: C — 3 m/s²

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Q. A 2 kg block is pulled with a force of 10 N. What is the frictional force if the block accelerates at 3 m/s²?

A. 4 N
B. 6 N
C. 10 N
D. 8 N

Solution

Net force = mass * acceleration = 2 kg * 3 m/s² = 6 N. The applied force is 10 N, so frictional force = applied force - net force = 10 N - 6 N = 4 N.

Correct Answer: B — 6 N

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Q. A 2 kg object moving at 10 m/s collides with a 3 kg object at rest. What is the total momentum before the collision?

A. 20 kg·m/s
B. 10 kg·m/s
C. 30 kg·m/s
D. 15 kg·m/s

Solution

Total momentum = momentum of 2 kg object + momentum of 3 kg object = (2 kg × 10 m/s) + (3 kg × 0 m/s) = 20 kg·m/s.

Correct Answer: A — 20 kg·m/s

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Q. A 3 kg object is moving with a momentum of 12 kg·m/s. What is its velocity?

A. 4 m/s
B. 3 m/s
C. 2 m/s
D. 1 m/s

Solution

Momentum (p) = mass (m) × velocity (v) => velocity (v) = p/m = 12 kg·m/s / 3 kg = 4 m/s.

Correct Answer: A — 4 m/s

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Q. A 3 kg object is moving with a velocity of 10 m/s. What is its momentum?

A. 15 kg·m/s
B. 30 kg·m/s
C. 10 kg·m/s
D. 5 kg·m/s

Solution

Momentum = mass × velocity = 3 kg × 10 m/s = 30 kg·m/s.

Correct Answer: B — 30 kg·m/s

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Q. A 4 kg object is moving at 6 m/s. If it collides with a wall and comes to a stop, what is the impulse experienced by the object?

A. 24 Ns
B. 12 Ns
C. 6 Ns
D. 30 Ns

Solution

Impulse (J) = change in momentum = mass (m) × change in velocity (Δv) = 4 kg × (0 - 6 m/s) = -24 Ns.

Correct Answer: A — 24 Ns

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Q. A 5 kg object is moving at a velocity of 3 m/s. What is its momentum?

A. 15 kg·m/s
B. 5 kg·m/s
C. 3 kg·m/s
D. 10 kg·m/s

Solution

Momentum (p) = mass (m) × velocity (v) = 5 kg × 3 m/s = 15 kg·m/s.

Correct Answer: A — 15 kg·m/s

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Q. A ball is dropped from a height of 45 meters. How long will it take to hit the ground? (Assume g = 9.8 m/s²)

A. 2 s
B. 3 s
C. 4 s
D. 5 s

Solution

Using the formula t = √(2h/g), where h = 45 m and g = 9.8 m/s², we get t = √(2 * 45 / 9.8) ≈ 3.06 s.

Correct Answer: C — 4 s

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Q. A ball is thrown horizontally from a height of 45 m. How long does it take to hit the ground? (Assume g = 9.8 m/s²)

A. 2 s
B. 3 s
C. 4 s
D. 5 s

Solution

Using the formula t = √(2h/g), where h = 45 m and g = 9.8 m/s², we get t = √(2 * 45 / 9.8) ≈ 3.03 s.

Correct Answer: C — 4 s

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Q. A boat is moving across a river at a speed of 8 km/h, while the river flows at 3 km/h. What is the resultant speed of the boat relative to the riverbank?

A. 5 km/h
B. 8 km/h
C. 9 km/h
D. 11 km/h

Solution

The resultant speed is found using the Pythagorean theorem: √(8^2 + 3^2) = √(64 + 9) = √73 ≈ 8.6 km/h.

Correct Answer: C — 9 km/h

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Q. A boat is moving upstream at a speed of 10 km/h in a river that flows downstream at 5 km/h. What is the speed of the boat relative to the riverbank?

A. 5 km/h
B. 10 km/h
C. 15 km/h
D. 0 km/h

Solution

The speed of the boat relative to the riverbank is the speed of the boat minus the speed of the river: 10 km/h - 5 km/h = 5 km/h.

Correct Answer: A — 5 km/h

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Q. A car accelerates from rest to 20 m/s in 5 seconds. What is the average acceleration?

A. 2 m/s²
B. 4 m/s²
C. 5 m/s²
D. 10 m/s²

Solution

Average acceleration is calculated as (final velocity - initial velocity) / time = (20 m/s - 0 m/s) / 5 s = 4 m/s².

Correct Answer: B — 4 m/s²

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Q. A car is traveling at 60 km/h on a straight road. If another car is moving in the same direction at 80 km/h, what is the speed of the second car relative to the first car?

A. 20 km/h
B. 60 km/h
C. 80 km/h
D. 140 km/h

Solution

The speed of the second car relative to the first car is 80 km/h - 60 km/h = 20 km/h.

Correct Answer: A — 20 km/h

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Q. A car of mass 1000 kg comes to a stop from a speed of 20 m/s. What is the impulse experienced by the car?

A. 20000 Ns
B. 10000 Ns
C. 5000 Ns
D. 40000 Ns

Solution

Impulse (J) = change in momentum = mass (m) × change in velocity (Δv) = 1000 kg × (0 - 20 m/s) = -20000 Ns.

Correct Answer: A — 20000 Ns

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Q. A child is riding a bicycle at 5 m/s on a moving bus that travels at 15 m/s in the same direction. What is the child's speed relative to the ground?

A. 10 m/s
B. 15 m/s
C. 20 m/s
D. 5 m/s

Solution

The child's speed relative to the ground is 15 m/s + 5 m/s = 20 m/s.

Correct Answer: C — 20 m/s

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Q. A child swings a ball attached to a string in a horizontal circle. If the radius of the circle is 2 m and the ball has a mass of 0.5 kg, what is the tension in the string if the ball moves at a speed of 4 m/s?

A. 2 N
B. 4 N
C. 8 N
D. 10 N

Solution

Tension provides the centripetal force: T = mv²/r = 0.5 kg * (4 m/s)² / 2 m = 8 N.

Correct Answer: C — 8 N

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Q. A cyclist accelerates from rest to a speed of 15 m/s in 10 seconds. What is the cyclist's acceleration?

A. 1.5 m/s²
B. 2 m/s²
C. 3 m/s²
D. 4 m/s²

Solution

Acceleration = (final velocity - initial velocity) / time = (15 m/s - 0) / 10 s = 1.5 m/s².

Correct Answer: B — 2 m/s²

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Q. A cyclist is riding at 15 km/h on a road that is moving at 5 km/h in the same direction. What is the cyclist's speed relative to the ground?

A. 10 km/h
B. 15 km/h
C. 20 km/h
D. 5 km/h

Solution

The cyclist's speed relative to the ground is 15 km/h + 5 km/h = 20 km/h.

Correct Answer: C — 20 km/h

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Q. A cyclist travels 100 meters in 5 seconds. What is the average speed of the cyclist?

A. 10 m/s
B. 15 m/s
C. 20 m/s
D. 25 m/s

Solution

Average speed = total distance / total time = 100 m / 5 s = 20 m/s.

Correct Answer: A — 10 m/s

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Q. A cyclist travels at 15 km/h on a road that is moving at 5 km/h in the same direction. What is the cyclist's speed relative to the road?

A. 10 km/h
B. 15 km/h
C. 20 km/h
D. 5 km/h

Solution

The cyclist's speed relative to the road is simply the speed of the cyclist: 15 km/h.

Correct Answer: B — 15 km/h

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Q. A disk is rolling without slipping. If its radius is 0.5 m and it has a linear speed of 2 m/s, what is its angular speed?

A. 2 rad/s
B. 4 rad/s
C. 6 rad/s
D. 8 rad/s

Solution

Using v = rω, we have ω = v/r = 2 m/s / 0.5 m = 4 rad/s.

Correct Answer: B — 4 rad/s

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Q. A flywheel is spinning with an angular velocity of 12 rad/s. If it experiences a constant angular deceleration of 3 rad/s², how long will it take to come to rest?

A. 2 s
B. 4 s
C. 6 s
D. 8 s

Solution

Using ω = ω₀ + αt, we set ω = 0, thus 0 = 12 rad/s - 3 rad/s² * t, giving t = 4 s.

Correct Answer: C — 6 s

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Q. A force of 30 N is applied at an angle of 60 degrees to the horizontal. What is the horizontal component of the force?

A. 15 N
B. 30 N
C. 25 N
D. 20 N

Solution

Horizontal component = F cos(θ) = 30 N × cos(60°) = 30 N × 0.5 = 15 N.

Correct Answer: D — 20 N

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Q. A machine does 200 J of work in 10 seconds. What is its power output?

A. 20 W
B. 30 W
C. 40 W
D. 50 W

Solution

Power = Work / Time = 200 J / 10 s = 20 W.

Correct Answer: A — 20 W

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Q. A machine does 200 J of work in 5 seconds. What is its power output?

A. 20 W
B. 40 W
C. 50 W
D. 60 W

Solution

Power = Work / Time = 200 J / 5 s = 40 W.

Correct Answer: B — 40 W

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Q. A person is running at 10 m/s on a moving walkway that moves at 2 m/s in the same direction. What is the person's speed relative to a stationary observer?

A. 8 m/s
B. 10 m/s
C. 12 m/s
D. 2 m/s

Solution

The person's speed relative to a stationary observer is the sum of their speeds: 10 m/s + 2 m/s = 12 m/s.

Correct Answer: C — 12 m/s

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Q. A person walks at a speed of 4 km/h on a train moving at 60 km/h in the same direction. What is the person's speed relative to the ground?

A. 64 km/h
B. 56 km/h
C. 60 km/h
D. 4 km/h

Solution

The person's speed relative to the ground is the speed of the train plus the speed of the person: 60 km/h + 4 km/h = 64 km/h.

Correct Answer: A — 64 km/h

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Mechanics

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