Question

What is the work done against gravity when the body of mass 10kg is moved horizontally along a frictionless surface $\left( {g = 10} \right)$

Answer 1

Hint Examine the direction of the force applied to the body of mass 10 kg. If there is no motion in the direction of force (which in our case is the direction opposite to that of gravity) then there is work done.

Complete step-by-step solution
When a body of mass m is pushed along a surface with coefficient of friction as $\mu$ , then the force of friction acting on the body in the direction opposite to the direction of motion is:

$$F = \mu R \\\ F = \mu (mg) \\\$$

If the surface is frictionless, it means that the coefficient of friction is 0, this means that the force of friction is also 0 in that case. Therefore, there is no force acting on the block in the direction opposite to the motion. However, there is one force acting on the body which is pulling it towards the center of the earth. This force is called the force due to gravity and acts vertically downwards to the body. Work done by any force is given by
$W = Fx\cos \theta$
Where F the force acting on that object
X is the distance travelled by the object
$\theta$ is the angle between the force and the direction of motion.
As in this question, the force is acting downwards and the motion is happening in the horizontal direction, $\theta$ will be 90 and $\theta$ will be 0. Therefore, no work is done by or against gravity

Note Work is said to be done if it satisfies two conditions. First, the force exerted on the object should cause displacement. Second, the force acting on the body should not be perpendicular to the direction of motion because the angle is 90 and cos90 is zero. Hence, no work is done.