COM of Solid Bodies

Q.

A block of mass M has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surfaced of a fixed table. Initially the right edge of the block is at x = 0, in a coordinate system fixed to the table. A point mass m is released from rest at the topmost point of the path as shown and it slides down. When the mass loses contact with the block, its position is x and the velocity is v. At that instant, which of the following option is/are correct ?

1. The velocity of the point mass m is $v=\sqrt{\frac{2gR}{1+\frac{m}{M}}}$.

2. The x component of displacement of the centre of mass of the block M is $-\frac{mR}{M+m}$.

3. The position of the point mass is x= $-\sqrt{2}\frac{mR}{M+m}$.

4. The velocity of the block M is V= $-\frac{m}{M}\sqrt{2gR}$.

Q.

We know centre of mass of a body can lie outside of the body, like in case of a ring. Now let’s take a semicircular ring whose centre is at 0, 0. Find the coordinate of it's center of mass.

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

2. $\frac{2R}{\pi }$

3. $\frac{R}{2}$

4. $\frac{8R}{\pi }$

Q.

We know centre of mass of a body can lie outside of the body, like in case of a ring. Now let’s take a semicircular ring whose centre is at 0, 0. Find the coordinate of it's center of mass.

1. $\frac{R}{2}$

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

3. $\frac{8R}{\pi }$

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

Q.

A block of mass M has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surfaced of a fixed table. Initially the right edge of the block is at x = 0, in a coordinate system fixed to the table. A point mass m is released from rest at the topmost point of the path as shown and it slides down. When the mass loses contact with the block, its position is x and the velocity is v. At that instant, which of the following option is/are correct ?

1. The velocity of the point mass m is $v=\sqrt{\frac{2gR}{1+\frac{m}{M}}}$.

2. The x component of displacement of the centre of mass of the block M is $-\frac{mR}{M+m}$.

3. The position of the point mass is x= $-\sqrt{2}\frac{mR}{M+m}$.

4. The velocity of the block M is V= $-\frac{m}{M}\sqrt{2gR}$.

Q.

Figure shows a uniform disc of radius R, from which a hole of radius $\frac{R}{2}$ has been cut out from left of the center and is placed on right of the center of disc. Find the centre of mass of the resulting disc.

1. 

2. 

3. 

4. 

Q.

lf all the particles of a system lie in a cube, is it necessary that the centre of mass be in the cube?

1. yes

2. No

3. some times

4. may be

Q.

Find the center of mass with respect to 0, of uniform semicircular wire of mass M and Radius R (as shown in figure)

1. 

2. 

3. 

4. 

Q.

Half of the rectangular plate shown in figure is made of a material of density $p_1$ and the other half of density $p_2$. The length of the plate is $L$. Locate the centre of mass of the plate.

1. 

2. 

3. 

4. 

Q.

Locate the COM of a uniform hemisherical solid with respect to 0 as shown in figure. (Radius = r)

1. 

2. 

3. 

4. 

Q.

Seven homo genous bricks , each of length $L$ , are arranged as shown below. Each brick is displaced with respect to the one in contact by $\frac{L}{10}$. Find $X$ coordinate of the centre of mass relative to the origin shown

1. 

2. 

3. 

4. None of these