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Course by: Sunil Kumar Singh. E-mail the author

# Laws of motion and system of particles (check your understanding)

Module by: Sunil Kumar Singh. E-mail the author

Summary: Objective questions, contained in this module with hidden solutions, help improve understanding of the topics covered under the module "Laws of motion and system of particles".

The questions have been selected to enhance understanding of the topics covered in the module titled " Laws of motion and system of particles ". All questions are multiple choice questions with one or more correct answers. There are two sets of the questions. The “understanding level” questions seek to unravel the fundamental concepts involved, whereas “application level” are relatively difficult, which may interlink concepts from other topics.

Each of the questions is provided with solution. However, it is recommended that solutions may be seen only when your answers do not match with the ones given at the end of this module.

## Understanding level (Laws of motion and system of particles)

### Exercise 1

A spherical object placed on a smooth horizontal table is at rest. It suddenly breaks in two unequal parts as a result of chemical reaction taking place inside the object. Then, the parts of the object move :

(a) in same direction

(b) in different directions

(c) in opposite directions with equal speeds

(d) in opposite directions with unequal speeds

### Exercise 2

In a system of two particles of 0.1 kg and 0.2 kg, The particle of 0.1 kg is at rest, whereas other particle moves with an acceleration "a". The magnitude of acceleration of the COM of the system of two particles is :

(a) a 3 (b) 2 a 3 (c) 3 a 2 (d) a 3 (a) a 3 (b) 2 a 3 (c) 3 a 2 (d) a 3

### Exercise 3

A sphere of radius "r" with uniform density is placed on a smooth horizontal surface. A horizontal force "F" is applied on the sphere. The acceleration of the center of sphere :

(a) is maximum when force is applied near the bottom edge of the sphere.

(b) is maximum when force is applied near the top edge of the sphere.

(c) is maximum when force is applied at middle of the sphere.

(d) is independent of position of application.

### Exercise 4

Two blocks of masses "m" and "2m" are released from rest as shown in the figure. The displacement of the COM of the block system (in meters) after 1 second is (neglect friction and masses of string and pulley) :

(a) 0.51 (b) 0.61 (c) 0.71 (d) 0.81 (a) 0.51 (b) 0.61 (c) 0.71 (d) 0.81

### Exercise 5

A block of mass "m" is released from the top of an incline of mass "M" as shown in the figure, where all the surfaces in contact are frictionless. The displacement of the incline, when the block has reached bottom is :

(a) m L m + M (b) m M L m + M (c) m L M - m (d) m M L M - m (a) m L m + M (b) m M L m + M (c) m L M - m (d) m M L M - m

## Application level (Laws of motion and system of particles)

### Exercise 6

Two particles are projected with speeds v 1 v 1 and v 2 v 2 making angles θ 1 θ 1 and θ 2 θ 2 with horizontal at the same instant as shown in the figure. Neglecting air resistance, the trajectory of the COM of the two particles :

(a) can be a vertical straight line

(b) can be a horizontal straight line

(c) is a straight line

(d) is a parabola

### Exercise 7

The wedge "C" is placed on a smooth horizontal plane. Two blocks "A" and "B" connected with "mass-less" string is released over a double sided wedge "C". The masses of blocks "A","B" and "C" are m, 2m and 3m respectively. After the release of the blocks, the block "B" moves on the incline by 10 cm, before it is stopped. Neglecting friction between all surfaces, the displacement of wedge "C", in the meantime, is (in cm):

(a) 5 (b) 5 2 (c) 5 2 2 (d) 10 (a) 5 (b) 5 2 (c) 5 2 2 (d) 10

### Exercise 8

Two blocks of equal mass are released over a fixed double incline as shown in the figure. Neglecting friction between incline and blocks, the acceleration of the COM of the blocks and double incline system is :

(a) 2 - 1 2 3 g (b) 2 + 1 4 3 g (c) 3 - 1 4 3 g (d) 3 + 1 2 3 g (a) 2 - 1 2 3 g (b) 2 + 1 4 3 g (c) 3 - 1 4 3 g (d) 3 + 1 2 3 g


1. (d)    2. (b)     3. (d)     4. (a)     5. (a)
6. (a)    7. (c)     8. (c)


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