Question 179: Centre of Mass and Rotational Motion

Question

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 :

Accepted Answer

$${\overrightarrow a _A} =  - a\widehat i$$;    $${\overrightarrow a _B} =  - a\widehat j$$
$${\overrightarrow a _C} =  - a\widehat i$$;    $${\overrightarrow a _D} =  - a\widehat j$$
$${\overrightarrow a _{cm}} = {{{m_a}{{\overrightarrow a }_a} + {m_b}{{\overrightarrow a }_b} + {m_c}{{\overrightarrow a }_c} + {m_d}{{\overrightarrow a }_d}} \over {{m_a} + {m_b} + {m_c} + {m_d}}}$$
$${\overrightarrow a _{cm}} = {{ - ma\widehat i + 2m\widehat j + 3ma\widehat i - 4ma\widehat j} \over {10m}}$$
= $${{2ma\widehat i - 2ma\widehat j} \over {10m}} = {a \over 5}\widehat i - {a \over 5}\widehat j = {a \over 5}\left( {\widehat i - \widehat j} \right)$$

Answer

$${a \over 5}\left( {\mathop i\limits^ \wedge   + \mathop j\limits^ \wedge  } \right)$$

Answer

$${a \over 5}\left( {\mathop i\limits^ \wedge   - \mathop j\limits^ \wedge  } \right)$$

Answer

$${a }\left( {\mathop i\limits^ \wedge + \mathop j\limits^ \wedge  } \right)$$

Answer

Zero

Centre of Mass and Rotational Motion

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 :

Choose the correct answer: