Mass m₁ moves on a slope making an angle θ with the horizontal and is attached to mass m₂ by a string passing over a frictionless pulley as shown in Fig. The co-efficient of friction between m₁ and the sloping surface is µ. Which of the following statements are true?

(a) If m₂ > m₁ sin θ , the body will move up the plane.

(b) If m₂ > m₁ (sin θ + µcos θ) , the body will move up the plane.

(c) If m₂ < m₁ (sin θ + µcos θ) , the body will move up the plane.

(d) If m₂ < m₁ (sin θ - µcos θ) , the body will move down the plane..

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

Answer- b, d

Explanation – as we know f = $\mu N=\mu m_{1}gcos\theta$

For system m₁+m₂ to move up

So m₂g- (m₁gsin $\theta +f$ )>0

So m₂g- (m₁gsin $\theta +\mu m_{1}gcos\theta$ )>0

So m₂>m₁ (sin $\theta +\mu cos\theta$ )

But if bodies moves downward

m₁gsin $\theta -f>m$ ₂g

m₁gsin> $\theta +\mu m_{1}gcos\theta$ m₂g

m₂1 (sinθ - uCosθ)

<p>This is a Multiple Choice Questions type Questions as classified in NCERT Exemplar</p><p><strong>Answer- b, d</strong></p><p><strong>Explanation </strong>– as we know f =<span contenteditable="false"> <math> <mi>μ</mi> <mi>N</mi> <mo>=</mo> <mi>μ</mi> <msub> <mrow> <mrow> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <mi>g</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>θ</mi> </math> </span></p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745402513phpgiUWsS_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745402513phpgiUWsS.jpeg" alt="" width="215" height="126"></picture></div></div><p>For system m₁+m₂ to move up</p><p>So m₂g- (m₁gsin<span contenteditable="false"> <math> <mi>θ</mi> <mo>+</mo> <mi>f</mi> </math> </span>)&gt;0</p><p>So m₂g- (m₁gsin<span contenteditable="false"> <math> <mi>θ</mi> <mo>+</mo> <mi>μ</mi> <msub> <mrow> <mrow> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <mi>g</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>θ</mi> </math> </span>)&gt;0</p><p>So m₂&gt;m₁ (sin<span contenteditable="false"> <math> <mi>θ</mi> <mo>+</mo> <mi>μ</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>θ</mi> </math> </span>)</p><p>But if bodies moves downward</p><p>m₁gsin<span contenteditable="false"> <math> <mi>θ</mi> <mo>-</mo> <mi>f</mi> <mo>&gt;</mo> <mi>m</mi> </math> </span>₂g</p><p>m₁gsin&gt;<span contenteditable="false"> <math> <mi>θ</mi> <mo>+</mo> <mi> </mi> <mi>μ</mi> <msub> <mrow> <mrow> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <mi>g</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>θ</mi> </math> </span>m₂g</p><p>m₂&lt;m_{1 (sinθ - uCosθ)&lt;/m}</p>

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