A rectangular block has a square base measuring a × a, and its height is h . It moves on a horizontal surface in a direction perpendicular to one of its edges. The coefficient of friction is μ. It will topple if

Question

A rectangular block has a square base measuring a × a, and its height is h . It moves on a horizontal surface in a direction perpendicular to one of its edges. The coefficient of friction is μ. It will topple if (A) μ >h / a (B) μ > a / h (C) μ >(2 a/h) (D) μ >(α/2 h)

Tardigrade Admin · Accepted Answer

As shown in figure normal reaction, R=m g . Frictional force, F=μ R=μ mg. To topple, clockwise moment must be more than the anticlockwise moment i.e., μ m g × (h/2)>m g × (a/2) or μ >a / h <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/e3807a3192f27e5ebf21e29570a52be7-.png" />

Q. A rectangular block has a square base measuring $a \times a$ , and its height is $h .$ It moves on a horizontal surface in a direction perpendicular to one of its edges. The coefficient of friction is $μ$ . It will topple if

$μ > h / a$

$μ > a / h$

$μ > \frac{2 a}{h}$

$μ > \frac{α}{2 h}$

As shown in figure normal reaction, $R = m g .$
Frictional force, $F = μ R = μ m g$ .
To topple, clockwise moment must be more than the anticlockwise moment
i.e., $μ m g \times \frac{h}{2} > m g \times \frac{a}{2}$
or $μ > a / h$

Q. A rectangular block has a square base measuring a×a, and its height is h. It moves on a horizontal surface in a direction perpendicular to one of its edges. The coefficient of friction is μ. It will topple if

μ>h/a

μ>a/h

μ>h2a​

μ>2hα​