COM of Center of Masses

Q. Two blocks of masses 3 kg and 1 kg are connected by a light string passing over a disc of mass 2 kg and radius 10 cm as shown in the figure. Then [Take g = 10 m/s²]
द्रव्यमान 3 kg तथा 1 kg के दो गुटकों को चित्रानुसार द्रव्यमान 2 kg तथा त्रिज्या 10 cm की डिस्क के ऊपर से गुजरने वाली हल्की डोरी द्वारा संयोजित किया जाता है। तब [g = 10 m/s² लीजिए]

1. Acceleration of centre of mass of the whole system is $\frac{8}{5}\hat{i}{\text{m/s}}^{\text{2}}$
   सम्पूर्ण निकाय के द्रव्यमान केंद्र का त्वरण $\frac{8}{5}\hat{i}{\text{m/s}}^{\text{2}}$ है
2. Acceleration of block of mass 3 kg is $-2\hat{i}{\text{m/s}}^{\text{2}}$
   द्रव्यमान 3 kg के गुटके का त्वरण $-2\hat{i}{\text{m/s}}^{\text{2}}$ है
3. Angular acceleration of pulley is 20 rad/s²
   घिरनी का कोणीय त्वरण 20 rad/s² है
4. Acceleration of block of mass 1 kg is $-2\hat{j}{\text{m/s}}^{\text{2}}$
   द्रव्यमान 1 kg के गुटके का त्वरण $-2\hat{j}{\text{m/s}}^{\text{2}}$ है

Q.

Find the centre of mass of uniform L-shaped lamina (a thin flat plate) with dimensions as shown in figure. The mass of lamina is 3 kg

1. 

2. 

3. 

4. 

Q.

A circular disc of radius R has a uniform thickness. A circular hole of diameter equal to the radius of the disc has been cut out as shown in figure. Find the centre of mass of the remaining disc.

1. units towards left

2. units towards Right

3. units towards left

4. units towards right

Q. A machinist starts with three identical square plates but cuts one corner from one of them, two corners from the second and three corners from the third. Rank the three according to the x - coordinates of their center of mass, from smallest to largest.

1. $3,1,2$
2. $1,3,2$
3. $3,2,1$
4. $1$ and $3$ tie, then $2$.

Q. A carpenter's square has the shape of an L as in figure, a force F is applied at distance x, find x for translatory motion of body.

1. 22 cm
2. 26 cm
3. 24 cm
4. 18 cm

Q. Three uniform bricks each of length $100\text{cm}$ and mass $m$ are arranged as shown in figure. The distance of centre of mass of the system of bricks from the wall is

1. $91\text{cm}$
2. $100\text{cm}$
3. $75\text{cm}$
4. $125\text{cm}$

Q. Five homogeneous bricks, each of length $L=9\text{m}$ are arranged as shown in the figure. Each of the bricks is displaced with respect to the next one in contact by $\frac{L}{6}$ as shown in the figure below. Find the $x-$ coordinate of the centre of mass relative to origin $\text{O}$.

1. $2.1\text{m}$
2. $5.4\text{m}$
3. $4.5\text{m}$
4. $6.3\text{m}$

Q. Three rectangular plates $A,B$ and $C$ made up of three different materials are joined together to form a large rectangular plate as shown in figure. If the densities of $A,B$ and $C$ are in the ratio $2:5:3$, then choose the correct option.

1. $COM$ lies inside $A$
2. $COM$ lies inside $B$
3. $COM$ lies inside $C$
4. $COM$ lies outside all three sheets

Q. Two equilateral triangular plates are joined together to form the following figure. Density of plate $A$ is $3$ times that of plate $B$. If $COM$ lies inside the plate $A$ at a distance $h=\sqrt{3}\text{m}$ from their common side, find out the length of side of each triangular plate.

1. $6\sqrt{3}\text{m}$
2. $3\sqrt{3}\text{m}$
3. $\frac{6}{\sqrt{3}}$
4. $12\text{m}$

Q. In the letter $E$ whose dimensions are given in the figure, origin is at the bottom left corner. Area of each rectangle is $12{\text{cm}}^2$ and area of the square is $4{\text{cm}}^2$. Assume that the weights are proportional to areas. Then, centre of gravity of the $E$ frame will be at:

1. $(1\text{cm},3\text{cm})$
2. $(2\text{cm},2\text{cm})$
3. $(2.4\text{cm},5\text{cm})$
4. $(3\text{cm},6\text{cm})$