In Fig , a body A of mass m slides on plane inclined at angle θ1 to the horizontal and µ1 is the coefficient of friction between A and the plane. A is connected by a light string passing over a frictionless pulley to another body B, also of mass m, sliding on a frictionless plane inclined at angle θ2 to the horizontal. Which of the following statements are true?

(a) A will never move up the plane.

(b) A will just start moving up the plane when µ= $\frac{\mathit{s}\mathit{i}\mathit{n}{\mathit{\theta }}_2-\mathit{s}\mathit{i}\mathit{n}{\mathit{\theta }}_1}{\mathit{c}\mathit{o}\mathit{s}{\mathit{\theta }}_1}$  .

(c) For A to move up the plane, θ₂ must always be greater than θ₁ .

(d) B will always slide down with constant speed.

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

Answer- b, c

Explanation- when A starts moving up

Mgsin ${\theta }_1+f=mgsin{\theta }_2$

mgsin ${\theta }_1$ + $\mu mgcos{\theta }_1$ = $mgsin{\theta }_2$

$\mu =\frac{\mathrm{s}\mathrm{i}\mathrm{n}{\mathrm{\theta }}_2-\mathrm{s}\mathrm{i}\mathrm{n}{\mathrm{\theta }}_1}{\mathrm{c}\mathrm{o}\mathrm{s}{\mathrm{\theta }}_1}$

When A moves downward f= $mgsin{\theta }_2-$ mgsin ${\theta }_1$ so clearly ${\theta }_2>{\theta }_1$

<p>This is a Multiple Choice Questions type Questions as classified in NCERT Exemplar</p><p><strong>Answer- b, c</strong></p><p><strong>Explanation- </strong>when A starts moving up</p><p>Mgsin<span contenteditable="false"> <math> <msub> <mrow> <mrow> <mi>θ</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <mo>+</mo> <mi>f</mi> <mo>=</mo> <mi>m</mi> <mi>g</mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <msub> <mrow> <mrow> <mi>θ</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </math> </span></p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745402577phpZeyICM_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745402577phpZeyICM.jpeg" alt="" width="219" height="94"></picture></div></div><p><strong>mgsin&nbsp;<math><msub><mrow><mrow><mi>θ</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math>&nbsp;+&nbsp;<math><mi>μ</mi><mi>m</mi><mi>g</mi><mi>c</mi><mi>o</mi><mi>s</mi><msub><mrow><mrow><mi>θ</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math>&nbsp;=&nbsp;<math><mi>m</mi><mi>g</mi><mi>s</mi><mi>i</mi><mi>n</mi><msub><mrow><mrow><mi>θ</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></math></strong></p><p><strong><math><mi>μ</mi><mo>=</mo><mfrac><mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mrow><mi mathvariant="normal">θ</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mrow><mi mathvariant="normal">θ</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></mrow></mrow><mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mrow><mi mathvariant="normal">θ</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></mrow></mrow></mfrac></math></strong></p><p><strong>When A moves downward f=&nbsp;<math><mi>m</mi><mi>g</mi><mi>s</mi><mi>i</mi><mi>n</mi><msub><mrow><mrow><mi>θ</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub><mo>-</mo></math>&nbsp;mgsin&nbsp;<math><msub><mrow><mrow><mi>θ</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math>&nbsp;so clearly&nbsp;<math><msub><mrow><mrow><mi>θ</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub><mo>&gt;</mo><msub><mrow><mrow><mi>θ</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math></strong></p>

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