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Tension in a String

If the surfac...

Question

If the surface shown in the figure is frictionless and the strings are inextensible, then the ratio of tensions $T_{1}$ and $T_{2}$ in the string is

A

3

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B

5

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C

12

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D

15

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Solution

The correct option is B $5$
Let $a$ be the horizontal acceleration of the whole system due to the horizontal component of force $F$ .
FBD of the $3 k g$ body

Using Newton's second law,
$\begin{matrix} T_{2} = m a = 3 a \\ (1) \end{matrix}$
FBD of $12 k g + 3 k g$ body,

Using Newton's second law,
$\begin{matrix} T_{1} = m a = 15 a \\ (2) \end{matrix}$
Dividing $(2)$ by $(1)$ , we get
$⟹ \frac{T_{1}}{T_{2}} = \frac{15 a}{3 a} = 5$

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