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Question: A body of mass \(40\;{\rm{gm}}\) is moving with a constant velocity \(2\;{{{\rm{cm}}} {\left/ {\vpha...

A body of mass 40  gm40\;{\rm{gm}} is moving with a constant velocity 2  cm/cmsecsec2\;{{{\rm{cm}}} {\left/ {\vphantom {{{\rm{cm}}} {{\rm{sec}}}}} \right. } {{\rm{sec}}}} on a horizontal frictionless table. The force on the table is-

Explanation

Solution

When a particle travels in a straight line and if the surface is smooth then there will be no force along the surface because there is no friction between the surface and the object. But the force in the perpendicular direction of the surface will act due the weight of the object and this force is termed as normal force.

Complete step-by-step solution:
The amount of the mass of the body is: m=40  gm = 40\;{\rm{g}}.
We know that one kilogram has 1000 g, so we will convert the unit into the kilogram by dividing the value of mass by .
The conversion of gram into kilogram is given as follows.
m=40  g×1  kg1000  g m=4×10−2  kg\begin{array}{l} m = 40\;{\rm{g}} \times \dfrac{{1\;{\rm{kg}}}}{{1000\;{\rm{g}}}}\\\ m = 4 \times {10^{ - 2}}\;{\rm{kg}} \end{array}
We know that the force on the table will be the equal to normal force.
The force on the table will work vertically downwards and it is equal to the weight of the body.
The expression for the weight of the body is given as follows,
w=mgw = mg
Here, mm is the mass of the body and gg is the acceleration of the body.
It is known that the acceleration of the gravity is 9.8  m/ms2s29.8\;{{\rm{m}} {\left/ {\vphantom {{\rm{m}} {{{\rm{s}}^{\rm{2}}}}}} \right. } {{{\rm{s}}^{\rm{2}}}}} .
Substitute all the values in the above expression.
w=4×10−2  kg×9.8  m/ms2s2 w=39.2×10−2  N\begin{array}{l} w = 4 \times {10^{ - 2}}\;{\rm{kg}} \times 9.8\;{{\rm{m}} {\left/ {\vphantom {{\rm{m}} {{{\rm{s}}^{\rm{2}}}}}} \right. } {{{\rm{s}}^{\rm{2}}}}}\\\ w = 39.2 \times {10^{ - 2}}\;{\rm{N}} \end{array}
Therefore, the force on the horizontal frictionless table is 39.2×10−2  N39.2 \times {10^{ - 2}}\;{\rm{N}} .

Note:
The Normal force is represented by NN and it is the force that acts on the body and applied by the surface, and it is a reaction force of the weight of the body. Newton's third law provides information about the action-reaction force, and it states that every applied force has a reaction force that acts in the opposite direction of the applied force and contains equal magnitude.