SATHEE: Rotational Motion Question 109

Rotational Motion Question 109

Question: The velocities of two particles $A$ and $B$ of same mass are ${\vec{V}}_{A} = a \vec{i}$ and ${\vec{V}}_{B} = b \hat{j}$ where $a$ and $b$ are constants. The acceleration of particle $A$ is $(2 a \hat{i} + 4 b \hat{j})$ and acceleration of particle $B$ is $(a \hat{i} - 4 b \hat{j}) ($ in $m / s^{2})$ . The centre of mass of two particle will move in

Options:

A) straight line

B) parabola

C) ellipse

D) circle

Show Answer

Answer:

Correct Answer: A

Solution:

[a]

${\vec{V}}_{com} = \frac{m_{1} {\vec{V}}_{1} + m_{2} {\vec{V}}_{2}}{m_{1} + m_{2}} = \frac{{\vec{V}}_{1} + {\vec{V}}_{2}}{2} = \frac{a \hat{i} + b \hat{j}}{2}$

${\vec{a}}_{c o m} = \frac{a_{1} + a_{2}}{2} = \frac{3}{2} (a \hat{i} + b \hat{j})$

${\vec{V}}_{c o m} is$ parallel to ${\vec{a}}_{com}$ .

Hence path will be a straight line.

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Rotational Motion Question 109

Question: The velocities of two particles A and B of same mass are V→A=ai→ and V→B=bj^ where a and b are constants. The acceleration of particle A is (2ai^+4bj^) and acceleration of particle B is (ai^−4bj^)( in m/s2). The centre of mass of two particle will move in

Options:

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Solution:

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