A uniform cube of mass m and side a is placed on a frictionless horizontal surface. A vertical force F is applied to the edge as shown in Fig. Match the following (most appropriate choice):

(a) mg/4 < F mg < /2 (i) Cube will move up.

(b) F > mg/2 (ii) Cube will not exhibit motion.

(c) F > mg (iii) Cube will begin to rotate and slip at A.

(d) F = mg/4 (iv) Normal reaction effectively at a/3 from A, no motion.

This is a short answer type question as classified in NCERT Exemplar

Moment of force $\tau$ ₁= F (a)….anticlockwise

Moment of weight mg $\tau$ ₂=mg (a/2)……. (clockwise)

Cube will not exhibit motion then $\tau$ _{1 $=\tau$ 2}

$F\times a=mg\times \frac{a}{2}$

F=mg/2

Cube will rotate when $\tau$ _{1 $>\tau$ 2}

$F\times a>mg\times \frac{a}{2}$

F>mg/2

At a/3 from point A then

mg $\times \frac{a}{3}=F\times aorF=\frac{mg}{3}$

when F=mg/4 which is less then mg/3 there will be no motion.

<p><span data-sheets-root="1">This is a short answer type question as classified in NCERT Exemplar</span></p><p>Moment of force <span contenteditable="false"> <math> <mi>τ</mi> </math> </span>₁= F (a)….anticlockwise</p><p>Moment of weight mg <span contenteditable="false"> <math> <mi>τ</mi> </math> </span>₂=mg (a/2)……. (clockwise)</p><p>Cube will not exhibit motion then <span contenteditable="false"> <math> <mi>τ</mi> </math> </span>_{1<span contenteditable="false"> <math> <mo>=</mo> <mi>τ</mi> </math> </span>}₂</p><p><span contenteditable="false"> <math> <mi>F</mi> <mo>×</mo> <mi>a</mi> <mo>=</mo> <mi>m</mi> <mi>g</mi> <mo>×</mo> <mfrac> <mrow> <mrow> <mi>a</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> </math> </span></p><p>F=mg/2</p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745468684php3ZmXAa_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745468684php3ZmXAa.jpeg" alt="" width="207" height="140"></picture></div></div><p>Cube will rotate when <span contenteditable="false"> <math> <mi>τ</mi> </math> </span>_{1<span contenteditable="false"> <math> <mo>&gt;</mo> <mi>τ</mi> </math> </span>}₂</p><p><span contenteditable="false"> <math> <mi>F</mi> <mo>×</mo> <mi>a</mi> <mo>&gt;</mo> <mi>m</mi> <mi>g</mi> <mo>×</mo> <mfrac> <mrow> <mrow> <mi>a</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> </math> </span></p><p>F&gt;mg/2</p><p>At a/3 from point A then</p><p>mg<span contenteditable="false"> <math> <mo>×</mo> <mfrac> <mrow> <mrow> <mi>a</mi> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </mfrac> <mo>=</mo> <mi>F</mi> <mo>×</mo> <mi>a</mi> <mi> </mi> <mi>o</mi> <mi>r</mi> <mi> </mi> <mi>F</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mi>m</mi> <mi>g</mi> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </mfrac> </math> </span></p><p>when F=mg/4 which is less then mg/3&nbsp;there will be no motion.</p>

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