# Center of mass and torque test for class 11

Center of mass
Torque and rotational mechanics

## Center of mass and torque test

Question 1 Write the expression for the position vector of the center of mass of n-particle system.

Question 2 Discus the motion of center of mass of the decay of radio-active nucleus into two parts.

Question 3 (a) Define the term torque (with the help of labeled diagram) . Give its units and dimensional formula. Show that it is product of force and its lever arm.

(b) State and explain the principle of moments of rotational equilibrium.

Question 4 Obtain expression for the work done by torque. Hence write the expression for power delivered by a torque.

Question 5 (a) Prove that the angular momentum of a particle is equal to twice the product of its mass and areal velocity.

(b) How does it lead to Kepler’s second law of planetary motion.

Question 6 Show that the area of the triangle contained between the vectors and is one half of the magnitude of .

Question 7 Find the torque of a force about the origin which acts on a particle whose position vector is .

Question 8 Torque and work are both equal to force times distance then how do they differ.

Question 9 Why is it easier to open a tap with two fingers than with one finger.

Question 10 Why do we prefer to use a wrench of longer arm.