Mechanics_Test-1

A particle under a conservative force moves from x=1 m to x=3 m. If the potential energy function is U(x)=5x², The work done by the force is:

• 40 J

• 80 J

• 50 J

• 20 J

Which of the following is an example of a non-conservative force?

• • Gravitational force

• • Electrostatic force

• • Magnetic force

• Force in elastic spring

The work-energy theorem states that the work done by all forces is equal to:

• • Total energy

• • Potential energy

• • Change in momentum

• • Change in kinetic energy

The mass of a solid sphere is M=5 kg, and its radius is R=50 cm. The moment of inertia of the sphere about an axis along its tangent is:

• 2.25 kg.m²

• 1.25 kg.m²

• 1.75 kg.m²

• 1.0 kg.m²

A ring and a disc of the same mass M and radius R rotate about their diameters. The ratio of their moments of inertia (I_ring/I_disc) is:

• 2

• 1

• 0.5

• 0.25

A solid cylinder of mass M and radius R rolls without slipping down an inclined plane making an angle of 30⁰ with the horizontal. The acceleration (a) of the cylinder down the incline is:

• g

Two objects of masses m₁ and m₂ collide elastically in one dimension. Initially, m₁​ is moving with speed u and m₂​ is at rest. After the collision, one-fourth of the initial kinetic energy of m₁ is transferred to m₂. The ratio of their masses m₁/m₂ is:

• 3

• a=1, b=1, c=6

• a=1, b=6, c=1

• a=6, b=1, c=6

• a=0, b=1, c=1

Three particles, each with a mass of 1 kg, are placed at the corners of an equilateral triangle with a side length of 2 m. The coordinates (x_cm, y_cm) of the center of mass of the system are:

• (1, 0)

• (1, 1)

An empty rocket weighs 10,000 kg and contains 90,000 kg of fuel. The exhaust velocity of the fuel is 2 km/s. The maximum velocity gained by the rocket is (Given: log_e 3 = ln⁡3 = 1.098, and log_e 10 = ln⁡10 = 2.3):

• 4.6 km/s

• 2.3 km/s

• 4.4 km/s

• 2.2 km/s