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Q.

A block of mass $\sqrt{3}$ kg rests on a horizontal frictionless xy-plane. What would be the acceleration of the block if it is subjected to two forces as shown in figure? (Assume acceleration due to gravity is along z- axis)

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a

2.5 ms^–2

b

5 ms^–2 along y-axis

c

10 ms^–2 along x-axis

d

15 ms^–2 along y-axis

answer is B.

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Detailed Solution

Horizontal component of 10 N is10 cos60° i. e. , $10 x \frac{1}{2} = 5 N$
It is balanced by 5 N force along x-axis.
Y-component of 10 N force is 10 sin60 N.
$\begin{matrix} i . e ., 10 \times \frac{\sqrt{3}}{2} N or 5 \sqrt{3} N \\ a_{y} = \frac{5 \sqrt{3} N}{\sqrt{3} kg} \\ = 5 {ms}^{- 2} \end{matrix}$

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