# Free NCERT Solutions For Class 11 Physics Chapter 7 : System of Particles and Rotational Motion Free PDF Download

**Question 1: Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body?**

**Solution 1:**

Geometric centre; No

The centre of mass (C.M.) is a point where the mass of a body is supposed to be concentrated.

For the given geometric shapes having a uniform mass density, the C.M. lies at their respective geometric centres.

The centre of mass of a body need not necessarily lie within it. For example, the C.M. of bodies such as a ring, a hollow sphere, etc., lies outside the body.

**Solution has been given in pdf**

**Question 3: A child sits stationary at one end of a long trolley moving uniformly with a speed V on a smooth horizontal floor. If the child gets up and runs about on the trolley in any manner, what is the speed of the CM of the (trolley + child) system?**

**Solution 3:**

No change

The child is running arbitrarily on a trolley moving with velocity v. However, the running of the child will produce no effect on the velocity of the centre of mass of the trolley. This is because the force due to the child’s motion is purely internal. Internal forces produce no effect on the motion of the bodies on which they act. Since no external force is involved in the (child+trolley) system, the child’s motion will produce no change in the speed of the centre of mass of the trolley.

**Question 4: Show that the area of the triangle contained between the vectors a and b is one half of themagnitude of a x b .**

**Solution has been given in pdf**

**Q 5 & 6 has been given in pdf**

**Question 7: Two particles, each of mass m and speed v, travel in opposite directions along parallel linesseparated by a distance d. Show that the vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is taken.**

**Solution has been given in pdf**

**Rest Questions are numerical that has been solved in given pdf**

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##### Free NCERT Solutions For Class 11 Physics Chapter 6 : Work, Energy and Power Free PDF Download

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