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Physics - Center of Mass Question with Solution | TestHub

PhysicsCenter of MassMotion of centre of massEasy2 minPYQ_2019

PhysicsEasysingle choice

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 is:

Options:

Answer:

Solution:

${\vec{a}}_{A} = - a \hat{i}$
${\vec{a}}_{B} = a \hat{j}$
${\vec{a}}_{C} = a \hat{i}$
${\vec{a}}_{D} = - a \hat{j}$
${\vec{a}}_{c m} = \frac{m_{a} {\vec{a}}_{a} + m_{b} {\vec{a}}_{b} + m_{c} {\vec{a}}_{c} + m_{d} {\vec{a}}_{d}}{m_{a} + m_{b} + m_{c} + m_{d}}$
${\vec{a}}_{c m} = \frac{- m a \hat{i} + 2 ma \hat{j} + 3 ma \hat{i} - 4 ma \hat{j}}{10 m}$

$= \frac{2 ma \hat{i} - 2 ma \hat{j}}{10,} = \frac{a}{5} \hat{i} - \frac{a}{5} \hat{j} = \frac{a}{5} (\hat{i} - \hat{j})$

Stream:JEESubject:PhysicsTopic:Center of MassSubtopic:Motion of centre of mass

⏱ 2mℹ️ Source: PYQ_2019

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