Question:

A force $F = 75\, N$ is applied on a block of mass $5\, kg$ along the fixed smooth incline as shown in figure. Here gravitational acceleration $g = 10m/s^2$. The acceleration of the block is

Updated On: Jan 18, 2023
  • $5 \frac{m}{s^{2}}$ downwards the incline
  • $5 \frac{m}{s^{2}}$ upwards the incline
  • $510 \frac{m}{s^{2}}$ downwards the incline
  • $10 \frac{m}{s^{2}}$ upwards the incline
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The Correct Option is D

Solution and Explanation

Consider the force acting on the block as shown below

Given, $F=75\, N$
$m=5\, kg$
Acceleration of the block
$F-m g \sin 30^{\circ} =m a$
$\Rightarrow a=\frac{F-m g \sin 30^{\circ}}{m}$
$\Rightarrow a =\frac{75-5 g \sin 30^{\circ}}{5}$
$a=\frac{50}{5}=10 m / s ^{2}$ upward to the inclined plane
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Concepts Used:

Newtons Laws of Motion

Newton’s First Law of Motion:

Newton’s 1st law states that a body at rest or uniform motion will continue to be at rest or uniform motion until and unless a net external force acts on it.

Newton’s Second Law of Motion:

Newton’s 2nd law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the object’s mass.

Mathematically, we express the second law of motion as follows:

Newton’s Third Law of Motion:

Newton’s 3rd law states that there is an equal and opposite reaction for every action.