Class 11th Overview Physics Physics Laws of Motion

For a free body diagram shown in the figure, the four forces are applied in the 'x' and 'y' directions. What additional forces must be applied and at what angle with positive x-axis so that the net acceleration of body is zero?

Option 1 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> <mi>N</mi> <mo>,</mo> <mn>4</mn> <mn>5</mn> <mo>°</mo> </mrow> </math> </span></p>

Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> <mi>N</mi> <mo>,</mo> <mn>1</mn> <mn>3</mn> <mn>5</mn> <mo>°</mo> </mrow> </math> </span></p>

Option 3 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>2</mn> </mrow> <mrow> <mroot> <mrow> <mn>3</mn> </mrow> <mrow></mrow> </mroot> </mrow> </mfrac> <mi>N</mi> <mo>,</mo> <mn>3</mn> <mn>0</mn> <mo>°</mo> </mrow> </math> </span></p>

Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mn>2</mn> <mi>N</mi> <mo>,</mo> <mn>4</mn> <mn>5</mn> <mo>°</mo> </mrow> </math> </span></p>

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Answered by

Payal Gupta | Contributor-Level 10

8 months ago

Correct Option - 1

Detailed Solution:

Let additional force is $\vec{F}$ , so

$\vec{F} + 5 (+ \hat{i}) + 6 (- \hat{i}) + 7 (+ \hat{j}) + 8 (- \hat{j}) = \vec{0}$

$\Rightarrow \vec{F} - (\hat{i} + \hat{j}) = \vec{0} \Rightarrow \vec{F} = \hat{i} + \hat{j} \Rightarrow F = \sqrt[]{2} N, 45 °$

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