Problem 66 - A Complete Resource Book in Physics for JEE Main

Question

A body of mass \(5 \mathrm{~kg}\) is acted upon by two perpendicular forces \(8 \mathrm{~N}\) and \(6 \mathrm{~N}\). Give the magnitude of the acceleration of the body. (A) \(2 \mathrm{~m} / \mathrm{s}^{2}\) (B) \(4 \mathrm{~m} / \mathrm{s}^{2}\) (C) \(6 \mathrm{~m} / \mathrm{s}^{2}\) (D) \(8 \mathrm{~m} / \mathrm{s}^{2}\)

Step-by-Step Solution

Answer

The short answer is: \(a = 2 \mathrm{~m} / \mathrm{s}^{2}\) (A).

Step 1: Determine the net force

We have two perpendicular forces acting on the body: 8 N and 6 N. To find the net force, the magnitude of the resultant force, we can use the Pythagorean theorem. F_net = √(F1^2 + F2^2) where F1 = 8 N, F2 = 6 N, and F_net is the magnitude of the net force acting on the body.

Step 2: Calculate the net force

Plug the values into the formula: F_net = √((8 N)^2 + (6 N)^2) = √(64 N^2 + 36 N^2) = √(100 N^2) = 10 N Now that we know the net force acting on the body, we can use Newton's second law to find the acceleration.

Step 3: Apply Newton's second law

Newton's second law states that force equals mass times acceleration (F = ma). We are given the mass (m = 5 kg) and we just found the net force (F_net = 10 N). Now we can solve for the acceleration (a) by rearranging the equation: a = F_net / m

Step 4: Calculate the acceleration

Plug in the known values into the equation: a = (10 N) / (5 kg) = 2 N/kg Acceleration has the units of meters per second squared (\(m/s^2\)), so the magnitude of the acceleration is 2 \(m/s^2\).

Step 5: Identify the correct answer choice

Now that we have found the magnitude of the acceleration, we can identify the correct answer choice as (A) \(2 \mathrm{~m} / \mathrm{s}^{2}\).