Question

In a system, 8 kg mass is subjected to a force of 16 N along positive y axis and another 8 N along positive x axis. The angle made by acceleration of centre of mass with x axis is

• A. \(45^\circ\)
• B. \(\theta=\tan^{-1}\!\left(\frac{2}{3}\right)\)
• C. \(\theta=\tan^{-1}(2)\)
• D. \(\theta=\tan^{-1}(\sqrt3)\)

Hint:

Angle of acceleration is same as angle of resultant force.

Answer 1

The Correct Option is C

Step 1: Resultant force on system: \[ F_x = 8\,\text{N}, \qquad F_y = 16\,\text{N}. \]
Step 2: Mass of system \(M = 16\) kg. Acceleration components: \[ a_x = \frac{8}{16}=0.5,\qquad a_y=\frac{16}{16}=1. \]
Step 3: Angle with \(x\) axis: \[ \tan\theta=\frac{a_y}{a_x}=\frac{1}{0.5}=2. \]
Step 4: \[ \theta=\tan^{-1}(2). \] Hence → (C).