Practice Questions

Acceleration in simple harmonic motion is directly proportional to the displacement of the particle. The equation for displacement of a particle in SHM is x = Asin( ωt) where A is the maximum displacement and  ω is the angular frequency. The acceleration of the particle is given by a = - ω2x

Co-efficient of friction between the road and vehicle contact point

The principle of conservation of mechanical energy states that the total mechanical energy in a system remains constant as long as the only forces acting are conservative forces. Mechanical energy is the sum of potential and kinetic energies. When a roller coaster car goes up a hill, its kinetic energy is converted to potential energy, which is then converted back to kinetic energy as the car descends. This principle applies to any system where only conservative force are acting

Principle of conservation of mechanical energy

A stone of mass "m" at the end of a string of length "L" is whirled in a vertical circle at a constant speed. the tension in the string will be maximum when the stone is at the bottom of the circle because the weight and and centrifugal force is aaded at this point.

Collisions can be elastic or inelastic. Momentum is conserved in all collisions, but inelastic collisions do not conserve kinetic energy. In a perfectly inelastic collision, objects stick together after the collision and move with the same velocity. This collision obeys the law of conservation of linear momentum.

The moment of a force about any point is the product of forces and perpendicular distance between the point and the line of action of force

There are two points P and Q on a planar rigid body.The relative velocity between the two points Should alwas perpendicular to PQ

Should be along QP when the body undergoes pure transilation

When a vehicle moves on a level circular path, the centripetal force generates with the help of friction between road and the tyres. As the center of mass of the car is above the level of the wheels of the vehicle, it tends to create a moment which will push the outer wheels in the downwarddirection and the inner wheels in the upward direction. Hence, the ground will exert a greater normal force on the outer wheels.

The reaction on the outer wheels will be more

The reaction on the inner wheels will be more

The reaction on the inner wheels as on the outer wheels will be equal

Difference between initial and final velocities

The rate of changeof momentum is equal to the applied force and it takes place in the direction of the force is a statement of Impluse -Momentum equation, also this lawisthe newton's second law

while going from groung to top the kinetic energy is converted in to potential energy so all points will be the same energy. at groung kinetic energy maximum and at the top potential energy is maximum.

Work done by conservative forces is equal to Decrease in potential energy

The study of Kinetics  provides the knowledge of inertia forces from the joint effect of the mass and motion of the components

A car moving in a straight line is does not follow any curved path under the action of gravitational force

A stone thrown horizondaly from abuilding

The range of projectile is maximum when the angle of projection is 45°

Law of conservation of Angular momentum
"if no external torque acts on a rigid body then the product of its moment of inertia and the angular velocity about the axis of rotation must remains constatnt"

The work done by a body moving down a smooth inclined plane is equal to the work done by the same body dropped vertically downward from the same height.
Using the equation W = force x displacement, we can calculate the work done in both cases. On the inclined smooth plane, the force along the plane is mg sine and the distance traveled is h / (sin theta) resulting in a work of mgh. Similarly, dropping the body vertically downward results in a work of mgh.

The path traced by a projectile in space is known asTrajectory

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