A mass of <math> <mn>10</mn> <mtext> </mtext> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">g</mi> </math> is suspended by a rope of length <math> <mn>4</mn> <mtext> </mtext> <mi mathvariant="normal">m</mi> </math> , from the ceiling. A force <math> <mi>F</mi> </math> is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of <math> <msup> <mrow> <mrow> <mn>45</mn> </mrow> </mrow> <mrow> <mrow> <mo>?</mo> </mrow> </mrow> </msup> </math> with the vertical. Then <math> <mi mathvariant="normal">F</mi> </math> equals: (Take <math> <mi mathvariant="normal">g</mi> <mo>=</mo> <mn>10</mn> <msup> <mrow> <mrow> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </mrow> </msup> </math> &nbsp;and the rope to be massless) &lt;!-- [if !supportLineBreakNewLine]--&gt; &lt;!--[endif]--&gt;

Ask & Answer Question

A mass of $10 k g$ is suspended by a rope of length $4 m$ , from the ceiling. A force $F$ is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of $45^{?}$ with the vertical. Then $F$ equals: (Take $g = 10 {m s}^{- 2}$ and the rope to be massless)

Option 1 -

$100 N$

Option 2 -

$75 N$

Option 3 -

$70 N$

Option 4 -

$90 N$

3 Views | Posted 2 months ago

Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 4

Detailed Solution:

$\frac{T}{\sqrt[]{2}} = 100 \frac{T}{\sqrt[]{2}} = F$

$F = 100 N$