What are the limitations of dimensional analysis?

What is Gross Error & How can it be minimised.

What do you understand by the term parallax angle?

The shadow of a pole standing on a level ground is found to be 45 m longer when the sun's altitude is 30^o than when it was 60^o. Determine the height of the pole. [Given \(\sqrt { 3 } \)=1.73]

Define
(i) unit vector
(ii) Orthogonal unit vectors.

Find the distance travelled by the particle during the time t = 0 to t = 3 seconds from the figure.

Consider an object travelling in a semi-circular path from point O to point P in 5 second, as is shown in the Figure. Calculate the average velocity and average speed.

Is the acceleration of a particle in circular motion not always towards the centre. Explain.

State Newton's third law.

A cricket ball of mass 35 g hits a stumps at an angle of 30° with a velocity of 20 m/s. If the ball rebounds at 60° the to the direction of incidence, calculate the impulse received by the cricket ball.

A bullet of mass 100gm is fired by a gun of 10 kg with a speed of 2000 m/sec. Find Recoil velocity of gun.

Determine the tensions T₁ and T₂ in the strings shown in the diagram.

Two springs A and B are identical except that A is harder than B (KA> KB) if these are stretched by the equal force. In which spring will more work be done?

A railway carriage of mass 9000 kg moving with a speed of 36 kmph collides with a stationary carriage of the same mass. After the collision, the carriages get coupled and move together. What is their common speed after the collision? What type of collision is this?

A particle of mass m is fixed to one end of a light spring of force constant k and unstretched length I. It is rotated with an angular velocity ω in horizontal circle. What will be the length increase in the spring?

State conservation of angular momentum. 

Two identical water bottles one empty and the other filled with water are allowed to roll down an inclined plane. Which one of them reaches the bottom first? Explain your answer.

A rectangle block rests on a horizontal table. A horizontal force is applied on the block at a height h above the table to move the block. Does the line of action of the normal force N exerted by the table on the block depend on h?

A uniform circular disc of mass m is set rolling on a smooth horizontal table with a uniform linear velocity v. Find the total K.E. of the disc.

Define gravitational potential energy.

What is meant by escape speed in the case of the Earth?