JEE Main 20198 AprilMorning Shift

Exam: JEE Main
Year: 2019
Date: 8 April
Shift: Morning Shift
Subject: Physics
Chapter: Center of Mass, Momentum and Collision

JEE Main 2019 · 8 April · Morning Shift · Physics · Center of Mass, Momentum and Collision

Four particles A, B, C and D with masses m _ A = m, m _ B = 2m, m _...

Four particles

A, B, C

and

D

with masses

{m}_{A} = m, {m}_{B} = 2m, {m}_{C} = 3m

and

{m}_{D} = 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 is:
Four particles A, B, C and D with masses m _ A = m, m _ B = 2m, m _ C = 3m and m _ D = 4m are at the corners of

Four particles A, B, C and D with masses m _ A = m, m _ B = 2m, m _ C = 3m  and m _ D = 4m are at the corners of

Options

A $\dfrac{a}{5}\left(\overset{^}{i} + \overset{^}{j}\right)$
B $\dfrac{a}{5}\left(\overset{^}{i} - \overset{^}{j}\right)$
C $a\left(\overset{^}{i} + \overset{^}{j}\right)$
DZero

Correct answer

B. $\dfrac{a}{5}\left(\overset{^}{i} - \overset{^}{j}\right)$

Step-by-step solution

Four particles A, B, C and D with masses m _ A = m, m _ B = 2m, m _ C = 3m and m _ D = 4m are at the corners of

$\overset{\to}{a}A = - a\overset{^}{i}$
$\overset{\to}{a}B = a\overset{^}{j}$
$\overset{\to}{a}C = a\overset{^}{i}$
$\overset{\to}{a}D = - a\overset{^}{j}$
$\overset{\to}{a}cm = \dfrac{{m}_{a}\overset{\to}{a}a + {m}_{b}\overset{\to}{a}b + {m}_{c}\overset{\to}{a}c + {m}_{d}\overset{\to}{a}d}{{m}_{a} + {m}_{b} + {m}_{c} + {m}_{d}}$
$\overset{\to}{a}cm = \dfrac{- ma\overset{^}{i} + 2ma\overset{^}{j} + 3ma\overset{^}{i} - 4ma\overset{^}{j}}{10m}$

$= \dfrac{2ma\overset{^}{i} - 2ma\overset{^}{j}}{10,} = \dfrac{a}{5}\overset{^}{i} - \dfrac{a}{5}\overset{^}{j} = \dfrac{a}{5}\left(\overset{^}{i} - \overset{^}{j}\right)$

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