# CBSE Class 11-Physics: Linear Momentum and System of Particles Assignment 1 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 1**:

(i) Two masses constrained to move in a horizontal plane collide. Given initially that , and . **i** and **j** are the unit vectors across x and y axis respectively

Find the velocity of center of mass

(a)

(b)

(c)

(d) None of the above

(ii) Find the total linear momentum of the system

(a)

(b)

(c)

(d) None of the above

(iii) . Find the velocity in the reference of frame in which center of mass is at rest

(a)

(b)

(c)

(d) None of the above

(iv) Let and are final velocity now we know and find the direction of

(a) with respect to x axis

(b) with respect to x axis

(c) with respect to x axis

(d) None of the above

**Answer**:

(i) – (a) : (ii) – (a) : (iii) – (b) : (iv) – (c)

**Question 2**:

A straight rod of length L has one of its end at origin and other at . If the mass per unit length of rod is . Find the centre of mass

(a)

(b)

(c)

(d) None of the above

**Answer**:

(a)

**Question 3**:

A uniform solid sphere has a spherical hole in it. Find the center of mass

(a)

(b)

(c)

(d) None of the above

**Answer**:

(a)

**Question 4**:

(i) Two mass and are joined by a rigid bar of negligible mass as shown in Figure

Being initially at rest, they are subjected to force and

Find the coordinate of their center of mass as a function of time

(a)

(b)

(c)

(d) None of the above

(ii) . Find the total linear momentum as function of time

(a)

(b)

(c)

(d) None of the above

**Answer**:

(i) - (b) : (ii) – (a)

**Question 5**:

A man of mass m standing is on a block of mass M. The system is at rest. The man moves relative in x direction to the block with velocity v ′ and then stops. Find the velocity of center of mass

(a)

(b)

(c)

(d) None of the above

**Answer**:

(b)

**Question 6**:

Three bodies form an isolated system. There are and . They have different direction, but all have the same initial speed v0. One or more elastic collision between the pair of the bodies where otherwise do not intersect. Find the maximum possible final speed of each of the three bodies.

(a)

(b)

(c)

(d) None of the above

**Answer**:

(c)

**Question 7**:

A ball is dropped from height h on a floor where coefficient of restitution is i.e.. Find the time required by the ball to stop rebounding

(a)

(b)

(c)

(d) None of the above

**Answer**:

(a)

**Question 8**:

**Matrix match type- In a system of particle**

Column A | Column A | ||

(a) | External force is present, but no internal force | (P) | Total momentum will remain constant |

(b) | Internal force is present, but no external force | (Q) | Total momentum will not remain constant |

(c) | Both no external and internal force | (R) | Centre of mass will accelerate |

(d) | Both internal and external force are present | (S) | Centre of mass will not accelerate |

**Answer**:

Matrix match type:

(a) ⇾ (Q) , (R)

(b) ⇾ (P) , (S)

(c) ⇾ (P) , (S)

(d) ⇾ (P) , (S)