A uniform solid cube of side a and mass M rests on a rough horizontal surface. A horizontal force F is applied at a height h from the base. Match the following conditions and critical values. List - I

Question

A uniform solid cube of side a and mass M rests on a rough horizontal surface. A horizontal force F is applied at a height h from the base. Match the following conditions and critical values. List - I List - II (P) The critical force F cr i t ​ at which toppling occurs, assuming no sliding, if h = a (1) M g /2 (Q) The critical force F cr i t ​ at which sliding occurs, assuming no toppling (2) μ s ​ M g (R) Condition for the cube to topple before sliding, if h = a (3) μ s ​ > 1/2 (S) Condition for the cube to slide before toppling, if h = a (4) μ s ​ < 1/2 (5) M g (6) 2 M g

TestHub · Accepted Answer

For toppling, the torque due to F about the edge must exceed the restoring torque due to M g . If h = a , F a > M g ( a /2 ) , so F cr i t , t o ppl e = M g /2 (P-1). For sliding, F > f ma x = μ s N = μ s M g , so F cr i t , s l i d e = μ s M g (Q-2). The cube topples before sliding if F cr i t , t o ppl e < F cr i t , s l i d e , which means M g /2 < μ s M g , implying μ s > 1/2 (R-3). The cube slides before toppling if F cr i t , s l i d e < F cr i t , t o ppl e , which means μ s M g < M g /2 , implying μ s < 1/2 (S-4).

List - I	List - II
(P) The critical force $F_{cr i t}$ at which toppling occurs, assuming no sliding, if $h = a$	(1) $M g /2$
(Q) The critical force $F_{cr i t}$ at which sliding occurs, assuming no toppling	(2) $μ_{s} M g$
(R) Condition for the cube to topple before sliding, if $h = a$	(3) $μ_{s} > 1/2$
(S) Condition for the cube to slide before toppling, if $h = a$	(4) $μ_{s} < 1/2$
	(5) $M g$
	(6) $2 M g$

Physics - Rotation Question with Solution | TestHub

Options:

Doubts & Discussion