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 figure. Match the Column I with Column II and mark the correct choice from the given codes. Column-I Column-II(i)Mg4 Mgr)Cube will begin to rotate and slip at,4.(iv)F = Mg4(s)Normal reaction effectively at a3 from A, no motionCodes

A
i -p, ii -q, iii-s, iv-r
B
i -r. ii - s, iii -q, iv-p
C
i - q, ii - r, iii - p, iv - s
D
i - s. ii -p, iii -r, iv-q

Solution:

From figure, Moment of force F about A,
$τ_{1} = F \times a$ , anticlockwise.
Moment of weight Mg of cube about A,
$τ_{2} = Mg \times \frac{a}{2}$ , clockwise
The cube will not exhibit any motion, if $τ_{1} = τ_{2}$
or F x a = $Mg \times \frac{a}{2} or F > \frac{Mg}{2}$
The cube will rotate only, when $τ_{1} > τ_{2}$
$F \times a > Mg \frac{a}{2} or F > \frac{Mg}{2}$
If we assume that normal reaction is effective at $\frac{a}{3}$ from A, then block would turn if
$Mg \times \frac{a}{3} = F \times a or F = \frac{Mg}{3}$

When F = $\frac{Mg}{4} < \frac{Mg}{3},$ there will be no motion.
Hence, we conclude (i) - q: (ii) - r; (iii) -p; (iv) - s.

Solution:

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