Question

Two blocks each of mass $m$ are resting on a frictionless inclined plane as shown in figure. Then which of the following statements about the blocks is correct?

$A)$ Block $A$ moves down the plane
$B)$ Block $B$ moves down the plane
$C)$ Both the blocks remain at rest
$D)$ Both the blocks moves down the plane

Answer 1

Hint : The gravitational force acting on an object is measured by its weight. It is determined by the mass of the object and the acceleration due to gravity, which on Earth is $9.8m{s^{ - 2}}$ .
$F = m \times 9.8m{s^{ - 2}}$ , where $F$ is the weight of the object in Newton $(N)$ and $m$ is the mass of the object in kilogram, is the formula for measuring weight.

Complete Step By Step Answer:
The component of weight responsible for the downward motion of the blocks is $mg\sin \theta$
The force acting on any object on an inclined plane will be,
$F = mg\sin \theta$
The force acting down the plane for block $A$ is,
${F_A} = mg\sin {60^ \circ } \\\ = \dfrac{{\sqrt 3 }}{2}mg \\\ = 0.866mg \\\$
The force acting down the plane for block $B$ is,
${F_B} = mg\sin {30^ \circ } \\\ = \dfrac{1}{2}mg \\\ = 0.5mg \\\$
Here, $0.866mg$ is greater than $0.5mg$ , therefore block $A$ moves down.
Since ${F_A} > {F_B}$ , block $A$ moves down the plane.
Therefore, the correct option is $A)$ Block $A$ moves down the plane.

Note :
On an inclined plane, the natural force is never equal to the object's weight (unless you consider the limiting case of the ground). It's proportional to the object's weight multiplied by the cosine of the inclined plane's angle with the horizontal.
To load and unload goods on trucks, cars, and planes, inclined planes are often used as loading ramps. Wheelchair ramps help people in wheelchairs overcome vertical barriers without exerting too much force. Inclined planes have escalators and slanted conveyor belts.