A body of mass 10kg is acted upon by two perpendicular forces, 6N and 8N. The resultant acceleration of the bo

NCERT Exemplar · Q15

Q. A body of mass 10kg is acted upon by two perpendicular forces, 6N and 8N. The resultant acceleration of the body is (Note: more than one of the given options may be correct.)

(a)

1

m s

^{-2}

at an angle of

\tan^{-1}\left(\dfrac{4}{3}\right)

w.r.t. 6N force.

(b)

0.2

m s

^{-2}

at an angle of

\tan^{-1}\left(\dfrac{4}{3}\right)

w.r.t. 6N force.

(c)

1

m s

^{-2}

at an angle of

\tan^{-1}\left(\dfrac{3}{4}\right)

w.r.t.8N force.

(d)

0.2

m s

^{-2}

at an angle of

\tan^{-1}\left(\dfrac{3}{4}\right)

w.r.t.8N force.

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Concept understanding — Newton Second Law

Newton's Second Law: The Law That Connects Force and Motion

Imagine you're pushing a shopping cart. If you push gently, it moves slowly. Push harder, and it speeds up faster. Now imagine the cart is full of groceries — even with the same push, it accelerates much more slowly than an empty cart. This everyday experience is exactly what Newton's Second Law captures.

The Intuition First

Two things matter when you push something:

How hard you push — the force you apply.
How heavy the object is — its mass.

The harder you push, the more the object speeds up. The heavier the object, the less it speeds up for the same push. So acceleration depends on both force and mass — and in opposite ways.

Note

"Acceleration" here means any change in velocity — speeding up, slowing down, or changing direction. It's not just "going faster."

The Precise Statement

Newton's Second Law says:

The acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to its mass. The acceleration is in the same direction as the net force.

In one equation:

\vec{a} = \frac{\vec{F}_{\text{net}}}{m}

Or more commonly:

\vec{F}_{\text{net}} = m \vec{a}

Where:

$\vec{F}_{\text{net}}$ is the net force (the vector sum of all forces acting on the object) — measured in newtons (N)
$m$ is the mass of the object — measured in kilograms (kg)
$\vec{a}$ is the acceleration — measured in metres per second squared ( $\text{m/s}^2$ )

\vec{F}_{\text{net}} = m \vec{a}

What This Really Means

Force causes acceleration, not velocity. A constant net force produces constant acceleration — meaning the velocity keeps changing at a steady rate. If you stop pushing, the net force becomes zero, and acceleration becomes zero (the object continues at constant velocity — that's Newton's First Law).

Mass is a measure of inertia. The more mass an object has, the harder it is to change its motion. A truck needs a much larger force than a bicycle to achieve the same acceleration.

Direction matters. Force and acceleration are vectors — they point the same way. If you push north, the acceleration is north. If multiple forces act, you must add them as vectors to find the net force.

A Simple Example

A 2 kg block is pushed with a net force of 10 N to the right.

a = \frac{F_{\text{net}}}{m} = \frac{10\ \text{N}}{2\ \text{kg}} = 5\ \text{m/s}^2

The block accelerates at $5\ \text{m/s}^2$ to the right. Every second, its velocity increases by 5 m/s in that direction. …

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Two perpendicular forces combine as vectors; their resultant divided by mass gives acceleration. The 10 N resultant force produces $1 \text{ m s}^{-2}$ at angle $\tan^{-1}(4/3)$ from the 6 N force.

When multiple forces act on a body, Newton's second law tells us that the net force determines the acceleration: $\vec{F}_{\text{net}} = m\vec{a}$ . The key insight is that forces are vectors—they add according to the parallelogram law, not simple arithmetic. Two perpendicular forces form the legs of a right triangle, and their resultant is the hypotenuse.

The direction of the acceleration is identical to the direction of the net force, and the magnitude scales inversely with mass. Let's find both the magnitude and direction systematically.

Finding the resultant force

Set up the geometry.

Place the 6 N force along one axis (say, horizontal) and the 8 N force perpendicular to it (vertical). Since they're perpendicular, we can use the Pythagorean theorem directly.
Calculate the magnitude of the resultant force.

F_{\text{net}} = \sqrt{(6)^2 + (8)^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \text{ N}

Find the direction of the resultant. The angle $\theta$ that the resultant makes with the 6 N force is given by:

\tan\theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{8}{6} = \frac{4}{3}

Therefore, $\theta = \tan^{-1}\left(\frac{4}{3}\right)$ with respect to the 6 N force.

Tip

When two perpendicular vectors have magnitudes in the ratio 3:4, their resultant is always in the ratio 5, forming a 3-4-5 Pythagorean triple. Here $6:8:10 = 3:4:5$ .

Finding the acceleration

Apply Newton's second law.

a = \frac{F_{\text{net}}}{m} = \frac{10 \text{ N}}{10 \text{ kg}} = 1 \text{ m s}^{-2}

Determine the direction of acceleration. The acceleration points in the same direction as the net force, so it makes an angle $\tan^{-1}(4/3)$ with the 6 N force.

Checking the angle with respect to the 8 N force

Alternative angle reference. If we measure the angle $\phi$ from the 8 N force instead, we use the complementary relationship: $\tan\phi = \frac{6}{8} = \frac{3}{4}$ …

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Q.A body of mass 10kg is acted upon by two perpendicular forces, 6N and 8N. The resultant acceleration of the body is (Note: more than one of the given options may be correct.)

Concept understanding — Newton Second Law

Newton's Second Law: The Law That Connects Force and Motion

The Intuition First

The Precise Statement

What This Really Means

A Simple Example

Finding the resultant force

Finding the acceleration

Checking the angle with respect to the 8 N force

Concept: Vector addition of perpendicular forces, then $F=ma$

Q.A body of mass 10kg is acted upon by two perpendicular forces, 6N and 8N. The resultant acceleration of the body is (Note: more than one of the given options may be correct.)

Finding the resultant force

Finding the acceleration

Checking the angle with respect to the 8 N force

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