September 2025 - Page 34 of 101

Titan, a satellite of Saturn, has a mean orbital radius of 1.22 × 10⁹ m. The orbital period of Titan is 15.95 days. Hyperion, another satellite of Saturn, orbits at a mean radius of 1.48 × 10⁹ m. Estimate the orbital period of Hyperion.

Introduction This problem uses Kepler’s Third Law, which relates the orbital period of a satellite to the radius of its orbit. Specifically, for satellites orbiting the same planet (Saturn in this case), the square of the orbital period is proportional to the cube of the orbital radius: (T₁/T₂)² = (R₁/R₂)³ Given Data Orbital radius of […]

Titan, a satellite of Saturn, has a mean orbital radius of 1.22 × 10⁹ m. The orbital period of Titan is 15.95 days. Hyperion, another satellite of Saturn, orbits at a mean radius of 1.48 × 10⁹ m. Estimate the orbital period of Hyperion. Read More »

At a crossing a truck travelling towards the north collides with a car travelling towards the east. After the collision the car and the truck stick together and move off at an angle of 30º east of north. If the speed of the car before the collision was 20 ms⁻¹, and the mass of the truck is twice the mass of the car, calculate the speed of the truck before and after the collision.

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Introduction This is a classic two-dimensional collision problem involving conservation of momentum. Since the truck and car stick together after collision, it’s an example of a perfectly inelastic collision. We will use vector components to solve for the unknown initial speed of the truck and the final velocity after the collision. Given Data Mass of

At a crossing a truck travelling towards the north collides with a car travelling towards the east. After the collision the car and the truck stick together and move off at an angle of 30º east of north. If the speed of the car before the collision was 20 ms⁻¹, and the mass of the truck is twice the mass of the car, calculate the speed of the truck before and after the collision. Read More »

A child of mass 50 kg is standing on the edge of a merry go round of mass 250 kg and radius 3.0 m which is rotating with an angular velocity of 3.0 rad s⁻¹. The child then starts walking towards the centre of the merry go round. What will be the final angular velocity of the merry go round when the child reaches the centre?

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Introduction This problem is based on the principle of conservation of angular momentum. When no external torque acts on a system, the total angular momentum remains constant. As the child moves toward the center, the system’s moment of inertia changes, which affects the angular velocity. Given Data Mass of child (m) = 50 kg Mass

A child of mass 50 kg is standing on the edge of a merry go round of mass 250 kg and radius 3.0 m which is rotating with an angular velocity of 3.0 rad s⁻¹. The child then starts walking towards the centre of the merry go round. What will be the final angular velocity of the merry go round when the child reaches the centre? Read More »

A girl is sitting with her dog at the left end of a boat of length 10.0 m. The mass of the girl, her dog and the boat are 60.0 kg, 30.0 kg and 100.0 kg respectively. The boat is at rest in the middle of the lake. Calculate the centre of mass of the system. If the dog moves to the other end of the boat, the girl staying at the same place, how far and in what direction does the boat move?

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Introduction This question is based on the principle of conservation of momentum and center of mass in a system with no external horizontal forces. Since the boat is on a lake, the system is isolated, and the center of mass of the system must remain unchanged in the absence of external forces. Given Data Mass

A girl is sitting with her dog at the left end of a boat of length 10.0 m. The mass of the girl, her dog and the boat are 60.0 kg, 30.0 kg and 100.0 kg respectively. The boat is at rest in the middle of the lake. Calculate the centre of mass of the system. If the dog moves to the other end of the boat, the girl staying at the same place, how far and in what direction does the boat move? Read More »

A horizontal rod with a mass of 10 kg and length 12 m is hinged to a wall at one end and supported by a cable which makes an angle of 30º with the rod at its other end. Calculate the tension in the cable and the force exerted by the hinge.

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Introduction This is a problem involving static equilibrium. The horizontal rod is supported at one end by a hinge and at the other end by a cable inclined at an angle. To solve this, we apply the conditions of equilibrium: Sum of all horizontal forces = 0 Sum of all vertical forces = 0 Sum

A horizontal rod with a mass of 10 kg and length 12 m is hinged to a wall at one end and supported by a cable which makes an angle of 30º with the rod at its other end. Calculate the tension in the cable and the force exerted by the hinge. Read More »

A wheel 2.0 m in diameter lies in the vertical plane and rotates about its central axis with a constant angular acceleration of 4.0 rad s⁻². The wheel starts at rest at t = 0 and the radius vector of a point A on the wheel makes an angle of 60º with the horizontal at this instant. Calculate the angular speed of the wheel, the angular position of the point A and the total acceleration at t = 2.0s.

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Introduction This problem involves rotational motion with constant angular acceleration. We’re asked to find the angular speed, angular position, and total acceleration of a point on the rim of a rotating wheel after 2 seconds. Given Data Diameter of wheel = 2.0 m ⇒ Radius (r) = 1.0 m Angular acceleration (α) = 4.0 rad/s²

A wheel 2.0 m in diameter lies in the vertical plane and rotates about its central axis with a constant angular acceleration of 4.0 rad s⁻². The wheel starts at rest at t = 0 and the radius vector of a point A on the wheel makes an angle of 60º with the horizontal at this instant. Calculate the angular speed of the wheel, the angular position of the point A and the total acceleration at t = 2.0s. Read More »

A box of mass 8.0 kg slides at a speed of 10 ms⁻¹ across a smooth level floor before it encounters a rough patch of length 3.0 m. The frictional force on the box due to this part of the floor is 70 N. What is the speed of the box when it leaves this rough surface? What length of the rough surface would bring the box completely to rest?

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Introduction This problem deals with the effect of friction on a moving object. When a box moves across a rough surface, the frictional force does negative work, reducing the speed of the box. We’ll apply the work-energy theorem to solve the two parts of this problem. Given Data Mass of box, m = 8.0 kg

A box of mass 8.0 kg slides at a speed of 10 ms⁻¹ across a smooth level floor before it encounters a rough patch of length 3.0 m. The frictional force on the box due to this part of the floor is 70 N. What is the speed of the box when it leaves this rough surface? What length of the rough surface would bring the box completely to rest? Read More »

A ball having a mass of 0.5 kg is moving towards the east with a speed of 8.0 ms⁻¹. After being hit by a bat it changes its direction and starts moving towards the north with a speed of 6.0 ms⁻¹. If the time of impact is 0.1 s, calculate the impulse and average force acting on the ball.

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Introduction This problem involves a change in the direction of motion of a ball due to a hit by a bat. Since the direction changes from east to north, we must deal with vector quantities. The concepts of impulse and average force are used here, which are based on the impulse-momentum theorem. Given Data Mass

A ball having a mass of 0.5 kg is moving towards the east with a speed of 8.0 ms⁻¹. After being hit by a bat it changes its direction and starts moving towards the north with a speed of 6.0 ms⁻¹. If the time of impact is 0.1 s, calculate the impulse and average force acting on the ball. Read More »

A crate of mass 30.0 kg is pulled by a force of 300 N up an inclined plane which makes an angle of 30º with the horizon. The coefficient of kinetic friction between the plane and the crate is μk = 0.225. If the crate starts from rest, calculate its speed after it has been pulled 15.0 m. Draw the free body diagram.

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Introduction In this problem, we are asked to calculate the final speed of a crate being pulled up an inclined plane with friction. To solve this, we apply Newton’s laws of motion and the work-energy theorem. We’ll also include a descriptive explanation of the free body diagram (FBD). Given Data Mass of crate, m =

A crate of mass 30.0 kg is pulled by a force of 300 N up an inclined plane which makes an angle of 30º with the horizon. The coefficient of kinetic friction between the plane and the crate is μk = 0.225. If the crate starts from rest, calculate its speed after it has been pulled 15.0 m. Draw the free body diagram. Read More »