Velocity of COM

Q. How mass increases with speed ?

Q.

Why does one get hurt seriously while jumping on a hard floor? Explain

Q.

Two particles A and B initially at rest, move towards each other by mutual force of attraction. At the instant when the speed of A is v and the speed of B is 2v, the speed of the centre of mass of the system is

1. 3v

2. v

3. 1.5 v

4. Zero

Q. For an object thrown vertically upwards, velocity is ________ at highest point.

1. infinite
2. zero
3. half its initial velocity
4. double its initial velocity

Q. Why it does not follow law of conservation of mass? 12g of C is heated in vacuum and on cooling there is no change in mass

Q. For an object thrown vertically upwards, velocity is ________ at highest point.

1. zero
2. half its initial velocity
3. double its initial velocity
4. infinite

Q.

Explain centrifugal force and centripetel force ??

Q. Four Particles of masses 1 kg, 2 kg, 3 kg, and 4 kg are placed at the corners of a square of side 2 m in the x – y plane in anticlockwise sense. If the origin of the co-ordinate system is taken at the mass of 1 kg, the (x, y) co-ordinates of the centre of mass, expressed in 'metre' are

1. $(3,\frac{7}{5})$
   
2. $(2,\frac{7}{5})$
   
3. $(1,\frac{7}{5})$
   
4. $(4,\frac{7}{5})$

Q.

Why makes earth to rotate on its axis

Q. Four particles of masses 'm', 'm', '2m' and '2m' are placed at the four corners of a square of side a as shown in diagram The (x, y) coordinates of the centre of mass are

1. $(a,\frac{a}{3})$
2. $(\frac{a}{2},\frac{2a}{3})$
   
3. $(\frac{a}{2},2a)$
   
4. $(\frac{a}{2},a)$
   

Q.

A nucleus moving with a velocity $\overrightarrow{v}$ emits an $\alpha$-p article. Let the velocities of the $\alpha$-particle and the remaining nucleus be $\overrightarrow{v_1}$ and $\overrightarrow{v_2}$ and their masses be $m_1$, and $m_2$ respectively. Choose the correct option.

1. , and must be parallel to each other.

2. None of the two of , and should be parallel to each other.

3. must be parallel to .

4. + must be parallel to .

Q. Choose the only incorrect statement from the following:

1. The angular momentum of a comet revolving around a massive star, remains constant over the centire orbit.
   
2. A body tied to a string is whirled in a circle with a uniform speed. If the string is suddenly cut, the angular momentum of the body will not change from its initial value.
3. The position of the centre of mass of a system of particles does not depend upon the internal forces between particles.
   
4. The centre of mass of a solid may lie outside the body of the solid.

Q. Four Particles of masses 1 kg, 2 kg, 3 kg, and 4 kg are placed at the corners of a square of side 2 m in the x – y plane in anticlockwise sense. If the origin of the co-ordinate system is taken at the mass of 1 kg, the (x, y) co-ordinates of the centre of mass, expressed in 'metre' are

1. 
   
2. 
   
3. 
   
4. 

Q.

Three particles of masses 0.50 kg, 1.0 kg and 1.5 kg are placed at the three corners of a right-angles triangle of sides 3.0 cm, 4.0 cm and 5.0 cm as shown in figure. Locate the centre of mass of the system taking O as origin

1. (1.3 cm, 1.5 cm)

2. (2.6 cm, 3cm)

3. (0.66 cm, 0.75 cm)

4. (2 cm, 2cm)

Q. In the HCl molecule, the separation between the nuclei of hydrogen and chlorine atoms is 1.27 $\stackrel{\circ }{A}$. If the mass of a chlorine atom is 35.5 times that of a hydrogen atom, the centre of mass of the HCl molecule is at a distance of

1. From the hydrogen atom
   
2. From the chlorine atom
   
3. From the hydrogen atom
4. From the chlorine atom

Q. Four particles of masses 'm', 'm', '2m' and '2m' are placed at the four corners of a square of side a as shown in diagram The (x, y) coordinates of the centre of mass are

1. 
   
2. 
   
3. 
4. 
   

Q. Four particles, each of mass 'm', are placed at the corners of 'a' square of side a in the x – y plane. If the origin of the co-ordinate system is taken at the point of intersection of the diagonals of the square, the co - ordinates of the centre of mass of the system are

1. (a, –a)
2. 0
3. (a, a)
4. (–a, a)

Q. Three particles, each of mass 'm', are placed at the corners of a right angled triangle as shown in Fig. If OA = a and OB = b, the position vector of the centre of mass is (here i and j are unit vectors along x and y axes respectively).

1. 
2. 
3. 
4. 
   

Q. Define conservation of linear momentum?

Q. Consider a rectangular plate of dimensions $a\times b$. If the plate is considered to be made up of four rectangles of dimensions $\frac{a}{2}\times \frac{b}{2}$ and we now remove one (the lower right) out of the four rectangles, find the position where the centre of mass of the remaining system will be (considering the center of the rectangular plate as the origin)

1. $\frac{a}{12},\frac{-b}{12}$
2. $\frac{a}{12},\frac{b}{12}$
3. $\frac{-a}{12},\frac{-b}{12}$
4. $\frac{-a}{12},\frac{b}{12}$

Q. A ball of mass 6.5 g is moving with a velocity of 2.5 m/s strikes with another ball of mass of 4.5 g. What is the combined velocity of both the balls?
(2 Marks)

Q. Rockets gain extremely high velocities due to conservation of momentum.

1. False
2. True

Q.

Calculate the velocity of the centre of mass of the system of particles shown in figure.

1. 0.2 m/s

2. 1 m/s

3. 0.8 m/s

4. 0.4 m/s

Q. A block of mass 5 kg is pushed up on a smooth inclined plane of angle of inclination 30 degree with help of a force of magnitude 50 N along the plane. The acceleration of the block will be

Q. In a vertical plane inside a smooth hollow thin tube a block of same mass as that of tube is released as shown in figure. When it is slightly disturbed, it moves towards right. By the time the block reaches the right end of the tube then the displacement of the tube will be (where 'R' is mean radius of tube). Assume that the tube remains in vertical plane.

1. $\frac{2R}{\pi }$
2. $\frac{4R}{\pi }$
3. R
4. $\frac{R}{2}$

Q.

The polar ice caps contain about 2.3 × 1019 kg of ice. This contributes essentially nothing to the moment of inertia of the earth because it is located at the poles, close to the axis of rotation. Estimate the change in the length of the day to be expected if the polar ice caps melt, distributing the water uniformly over the surface of the earth. Take mass of earth = 5.98 × 1024 kg and radius of earth = 6.37 × l06 m.