A body of mass 10kg is acted upon by two perpendicular forces, 6N and 8N. The resultant acceleration of the body is

(a) 1 m s^-2 at an angle of tan^-1(3/4) w.r.t. 6N force.

(b) 0.2 m s^-2 at an angle of tan^-1(3/4) w.r.t. 6N force.

(c) 1 m s^-2 at an angle of tan^-1(3/4) w.r.t.8N force.

(d) 0.2 m s^-2 at an angle of tan^-1(3/4) w.r.t.8N force.

This is a Multiple Choice Questions type Questions as classified in NCERT Exemplar

Answer- a, c

Explanation – mass m= 10kg

F₁ =6N, F₂= 8N

Resultant force F= $\sqrt[]{36+64}=10N$

a=f/m= 10/10= 1m/s²

let $\theta$ ₁ be the angle between R and F₁

tan $\theta$ ₁=8/6=4/3

_{$\theta$ 1}= tan $\theta$ ₁ (4/3) w.r.t F₁=6N

let $\theta$ ₂ be the angle between F and F₂

tan $\theta$ ₁=8/6=4/3

_{$\theta$ 2}= tan $\theta$ ₂ (4/3) w.r.t F₂=8N

<p>This is a Multiple Choice Questions type Questions as classified in NCERT Exemplar</p><p><strong>Answer- a, c</strong></p><p><strong>Explanation</strong> – mass m= 10kg</p><p>F₁ =6N, F₂= 8N</p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745402622phpEJuPat_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745402622phpEJuPat.jpeg" alt="" width="118" height="111"></picture></div></div><p>Resultant force F=<span contenteditable="false"> <math> <mroot> <mrow> <mrow> <mn>36</mn> <mo>+</mo> <mn>64</mn> </mrow> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mn>10</mn> <mi>N</mi> </math> </span></p><p>a=f/m= 10/10= 1m/s²</p><p>let<span contenteditable="false"> <math> <mi>θ</mi> </math> </span> ₁ be the angle between R and F₁</p><p>tan<span contenteditable="false"> <math> <mi>θ</mi> </math> </span>₁=8/6=4/3</p><p>_{<span contenteditable="false"> <math> <mi>θ</mi> </math> </span>1}= tan<span contenteditable="false"> <math> <mi>θ</mi> </math> </span>₁ (4/3) w.r.t F₁=6N</p><p>let <span contenteditable="false"> <math> <mi>θ</mi> </math> </span>₂ be the angle between F and F₂</p><p>tan<span contenteditable="false"> <math> <mi>θ</mi> </math> </span>₁=8/6=4/3</p><p>_{<span contenteditable="false"> <math> <mi>θ</mi> </math> </span>2}= tan<span contenteditable="false"> <math> <mi>θ</mi> </math> </span>₂ (4/3) w.r.t F₂=8N</p>

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