Question

Choose the wrong statements:
(A). $1kg\,wt=9.8N$
(B). Momentum is a vector quantity
(C). Force is always conserved
(D). Momentum is conserved in the absence of an external force

Answer 1

$kg\,wt$ is a unit used to represent gravitational force. Momentum is the product of mass and velocity. There are two types of forces depending on the path taken; conservative and non-conservative. When there are no external forces acting on a system, the system is said to be isolated.

Complete step-by-step solution:
$kg\,wt$ is one of the units of gravitational force. $1kg\,wt$ is the force of gravity acting on a body of ma$1kg$
Weight in Newtons will be-
$\begin{aligned} & mg=1\times 9.8N \\\ & \Rightarrow mg=9.8N \\\ \end{aligned}$
Therefore, the force of gravity on a body of mass $1kg$ in Newton in $9.8N$. Therefore,
$1kg\,wt=9.8N$ is correct.
Momentum is defined as the product of mass and velocity. Its SI unit is $kg\,m{{s}^{-1}}$. It is given by-
$p=mv$
Here, $p$ is momentum
$m$ is the mass of a body
$v$ is the velocity of the body
From the above equation, we can see that momentum is a scalar product of a scalar and a vector which is a vector quantity. Therefore, momentum is a vector quantity.
A force is conserved when it does not depend on the path taken. Forces like gravitational, electrostatic, and magnetic forces are conserved but the forces in mechanics are a product of mass and acceleration. Since the acceleration depends on the path taken, the mechanical forces are non-conservative in nature. Also, the frictional force also depends on the path, so it is also non-conserved.
Therefore, forces are not always conserved.
The law of conservation of momentum says that the initial and final momentum of an isolated system is zero. Since there will be no external forces, the bodies in the system will either remain at rest or in uniform motion. Hence, momentum is conserved in the absence of an external field.
Therefore, the forces are not always conserved. Hence, the correct option is (C).

Note: For an isolated system, the energy of the system is also conserved. According to Newton’s second law, force is required to change the state of rest or motion of a body. The magnitude of the acceleration due to gravity is $9.8m{{s}^{-2}}$. Conservative forces depend on the two points between which force acts and not on the path taken.