In Fig., the co-efficient of friction between the floor and the body B is 0.1. The co-efficient of friction between the bodies B and A is 0.2. A force F is applied as shownon B. The mass of A is m/2 and of B is m. Which of the following statements are true? 

(a) The bodies will move together if F = 0.25 mg.

(b) The body A will slip with respect to B if F = 0.5 mg.

(c) The bodies will move together if F = 0.5 mg.

(d) The bodies will be at rest if F = 0.1 mg.

(e) The maximum value of F for which the two bodies will move together is 0.45 mg.

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

Answer- a, b, d, e

Explanation- suppose A and B are moving together a_common= $\frac{F-f_1}{m_A+m_B}=\frac{2\left(F-t_1\right)}{3m}$

Pseudo force = m_A (a_common)= $\frac{m}{2}*$ $\frac{2\left(F-t_1\right)}{3m}$ = $\frac{F-t_1}{3}$

Force will be maximum when pseudo force and frictional force are equal to one another

$\frac{F_{max}-f_1}{3}$ = $?m_{A}g$

= 0.2 $*\frac{m}{2}*g=0.1mg$

F_max= 0.3mg+f₁

= 0.3mg+0.1 (3/2)mg= 0.45mg

(a) for F=0.25mgmax bodies will move together

(b) for F=0.5mg>F_max body A will slip with respect to B

(c) for F=0.5mg>F_max bodies will slip

<p>This is a Multiple Choice Questions type Questions as classified in NCERT Exemplar</p><p><strong>Answer- a, b, d, e</strong></p><p><strong>Explanation</strong>- suppose A and B are moving together a_common=<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>F</mi> <mo>-</mo> <msub> <mrow> <mrow> <mi>f</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mi>A</mi> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mrow> <mrow> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mi>B</mi> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>2</mn> <mfenced separators="|"> <mrow> <mrow> <mi>F</mi> <mo>-</mo> <msub> <mrow> <mrow> <mi>t</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfenced> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> <mi>m</mi> </mrow> </mrow> </mfrac> </math> </span></p><p>Pseudo force = m_A (a_common)<strong>=&nbsp;<math><mfrac><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></mfrac><mo>*</mo></math>&nbsp;<math><mfrac><mrow><mrow><mn>2</mn><mfenced separators="|"><mrow><mrow><mi>F</mi><mo>-</mo><msub><mrow><mrow><mi>t</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></mrow></mrow></mfenced></mrow></mrow><mrow><mrow><mn>3</mn><mi>m</mi></mrow></mrow></mfrac></math>&nbsp;=&nbsp;<math><mfrac><mrow><mrow><mi>F</mi><mo>-</mo><msub><mrow><mrow><mi>t</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></mfrac></math></strong></p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745402456php2WOO2k_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745402456php2WOO2k.jpeg" alt="" width="157" height="74"></picture></div></div><p>Force will be maximum when pseudo force and frictional force are equal to one another</p><p><span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>F</mi> </mrow> </mrow> <mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </mrow> </msub> <mo>-</mo> <msub> <mrow> <mrow> <mi>f</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </mfrac> </math> </span>=<span contenteditable="false"> <math> <mi>? </mi> <msub> <mrow> <mrow> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mi>A</mi> </mrow> </mrow> </msub> <mi>g</mi> </math> </span></p><p>= 0.2<span contenteditable="false"> <math> <mo>*</mo> <mfrac> <mrow> <mrow> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mo>*</mo> <mi>g</mi> <mo>=</mo> <mn>0.1</mn> <mi>m</mi> <mi>g</mi> </math> </span></p><p>F_max= 0.3mg+f₁</p><p>= 0.3mg+0.1 (3/2)mg= 0.45mg</p><p> (a) for F=0.25mg&lt;f_{max bodies will move together&lt;/f}</p><p> (b) for F=0.5mg&gt;F_max body A will slip with respect to B</p><p> (c) for F=0.5mg&gt;F_max bodies will slip</p>

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