Motion of systems of particles and rigid body: Physics

 

• Notes Of Motion of system of particle and rigid body

Q.1. The distance travelled by an object along a straight line in time t is given by  The initial velocity of the object is 

A) 3 unit

B) -3 unit 

C) 5 unit 

D) -5 unit 

Explanation-

          

         

Initial velocity, u= 

Q.2. Two particles of masses 1 kg and 3 kg have position vectors   respectively. The center of mass has a position vector 

A) 

B) 

C) 

D)  

Explanation-

Here, 

The position vector of center of mass is 

 

Q.3. Three bricks each of length L and M are arranged as shown from the wall. The distance of the center of mass of the system from the wall is

 

A) 

B) 

C) 

D)  

Explanation-

From figure , 

 

Q.4. Three particles, each of mass m, are placed at the corners of a right angled triangle as shown in figure. If OA = a and OB = b , the position vector of the center of mass is (Here    are unit vectors along x and y axes respectively ).

A) 

B) 

C) 

D)  

Explanation-

The (x , y ) co- ordinates of the masses at O, A and B respectively are ( refer to figure as given in the question ) 

 

Q.5. In a carbon monoxide molecule , the carbon and oxygen atom are separated by a distance of  m. The distance of the center of mass from the carbon atom is 

A) 

B) 

C) 

D)  

Explanation-

Since the mass of carbon atom is 12 units and that of oxygen atom is 16 units , the distance of the centre of mass from the carbon atom is 

 

Q.6. The centre of mass of three bodies each of mass 1 kg located at the points (0,0), (3,0) and (0, 4 ) in the x-y plane is 

A) 

B) 

C) 

D)  

Explanation-

Here , 

The coordinates of centre of mass are  .

Q.7. Particles of masses m, 2m, 3m... , nm gram are placed on the same line at distances l, 2l, 3l..., nl cm from a fixed point . The distance of centre of mass of the particles from the fixed point in centimeters is 

A)  

B) 

C) 

D)  A) 140 m

B) 40 m 

C) 100 m 

D) 360 m 

Explanation-

 

Q.8. A train moving with a speed of 36 km/h takes 14 s to cross a bridge of length 100 m. The length of the train is 

A) 140 m

B) 40 m 

C) 100 m 

D) 360 m 

Explanation-

Speed of train , v=36 km/h =10 m/s Let x meter be the length of train. 

Total distance to be travelled by train to cross the bridge = (x+100) m 

As distance = speed time 

 (x+100)=10 14 or x=40 m 

Q.9. The position of center of mass of a system of particles does not depend upon 

A) masses of particles

B) forces on particles 

C) position of the particles 

D) relative distance between the particles 

Explanation-

The position of center of mass of a system of particles does not depend upon the forces on the particles.

Q.10. Three particles of masses 1 kg, 2kg, and 3kf are situated at the corners of an equilateral triangle of side b in the x-y plane with mass 1kg  at the origin and 2 kg, on the x-axis. The coordinates of the center of mass are 

A) 

B) 

C) 

D)  

Explanation-

The coordinates of points A,B and C are (0,0) (b, 0) and  respectively. 

So, the coordinates of center of mass are 

  

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