Question

the linear momentum P of a body moving in one dimension varies with time according to the equation P=at^3 +bt where a and b are positive constant . The net force acting on the body is-
a) proportional to t^2
b) a constant
c) proportional to t
d) inversely proportional to t

Answer 1

Answer:

The correct answer is option a) proportional to $t^2$.

Explanation:

Concept:

The sum of a system's mass and velocity is known as its linear momentum. According to the formula $F = \frac{dp}{dt}$, the force exerted on a body is inversely related to the change in momentum. In this context, momentum is used to describe the amount of motion a body contains. In other words, the equation illustrates the idea that a force can alter a body's motion or state.

Given:

Linear momentum of a body = P

Time = t

Equation : $P=at^3 +bt$

Here $a$ and $b$ are positive.

To find:

We have to find the net force acting on the body.

Solution:

The given equation is:

$P=at^3 +bt$

$\frac{dP}{dt}=\frac{d(at^3 +bt)}{dt}$

$F = \frac{dP}{dt}$

$F=\frac{d(at^3 +bt)}{dt}$

$F=\frac{dt(at^2 +b)}{dt}$

$F=at^2 +b$

Thus $F$∝ $t^2$ is the correct answer.

#SPJ3