Question 46: Laws of Motion

Question

An object with mass 500 g moves along x-axis with speed $v = 4\sqrt{x}$ m/s. The force acting on the object is :

Accepted Answer

To find the force acting on the object, we use the formula $ F = m 	imes a $, where $ F $ is the force, $ m $ is the mass, and $ a $ is the acceleration.
The velocity $ v $ is given as $ v = 4 \sqrt{x} $.
Squaring both sides, we have $ v^2 = 16x $.
Differentiate $ v^2 $ with respect to $ x $:
$    2v \frac{dv}{dx} = 16    $
Solving for $ \frac{dv}{dx} $, we find:
$    \frac{v \, dv}{dx} = \frac{16}{2} = 8    $
The force $ F $ is then calculated as:
$    F = 0.5 	imes 8 = 4 \, 	ext{N}    $
Thus, the force acting on the object is 4 N.

Answer

8 N

Answer

4 N

Answer

5 N

Answer

6 N

Laws of Motion

An object with mass 500 g moves along x-axis with speed v = 4\sqrt{x} m/s. The force acting on the object is :

Choose the correct answer: