SATHEE: Centre of Mass 1 Question 3

Centre of Mass 1 Question 3

3. Four particles $A, B, C$ and $D$ with masses $m_{A} = m$ , $m_{B} = 2 m, m_{C} = 3 m$ and $m_{D} = 4 m$ are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles (in $m s^{- 2}$ ) is

(2019 Main, 8 April I)

(a) $\frac{a}{5} (\hat{i} - \hat{j})$

(b) $a (\hat{i} + \hat{j})$

(d) $\frac{a}{5} (\hat{i} + \hat{j})$

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Answer:

Correct Answer: 3. (a)

Solution:

For a system of discrete masses, acceleration of centre of mass (CM) is given by

$a_{C M} = \frac{m_{A} a_{A} + m_{B} a_{B} + m_{C} a_{C} + m_{D} a_{D}}{m_{A} + m_{B} + m_{C} + m_{D}}$

where, $m_{A} = m, m_{B} = 2 m, m_{C} = 3 m$ and $m_{D} = 4 m$ , $| a_{A} | = | a_{B} | = | a_{C} | = | a_{D} | = a$ (according to the question)

$\begin{aligned} a_{C M} = & \frac{- m a \hat{i} + 2 m a \hat{j} + 3 m a \hat{i} - 4 m a \hat{j}}{m + 2 m + 3 m + 4 m} \\ = \frac{2 a \hat{i} - 2 a \hat{j}}{10} = \frac{a}{5} \cdot (\hat{i} - \hat{j}) m s^{- 2} \end{aligned}$

Centre of Mass 1 Question 3

3. Four particles $A, B, C$ and $D$ with masses $m_{A} = m$ , $m_{B} = 2 m, m_{C} = 3 m$ and $m_{D} = 4 m$ are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles (in $m s^{- 2}$ ) is

Answer:

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Centre of Mass 1 Question 3

3. Four particles A,B,C and D with masses mA=m, mB=2m,mC=3m and mD=4m are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles (in ms−2 ) is

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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3. Four particles $A, B, C$ and $D$ with masses $m_{A} = m$ , $m_{B} = 2 m, m_{C} = 3 m$ and $m_{D} = 4 m$ are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles (in $m s^{- 2}$ ) is