Question

Two objects having their masses in ratio 3:5 are acted upon by two forces each on one object. The forces are in the ratio of 5:3. Find the ratio in their accelerations.

Answer 1

Answer:

• The Ratios of Acceleration (a₁ : a₂) is 25 : 9.

Given:

1. Ratio of Mass = 3 : 5
2. Ratio of Forces = 5 : 3

Explanation:

$\rule{300}{1.5}$

Let there be a Common Component be x between Acceleration.

Therefore,

• a₁ = 3x
• a₂ = 5x

Let there be a Common Component be x between Force.

Therefore,

• F₁ = 5x
• F₂ = 3x

From Newton's Second law of motion,

$\large\bigstar \: {\boxed{\tt F = Ma}}$

$\bold{Here}\begin{cases}\text{F Denotes Force Applied} \\ \text{M Denotes Mass} \\ \text{a Denotes Acceleration}\end{cases}$

Now,

$\large{\boxed{\tt F = Ma}}$

From General Notations of Force,

we get.

1. F₁ = M₁a₁ ----(1)
2. F₂ = M₂a₂ -----(2)

$\rule{300}{1.5}$

$\rule{300}{1.5}$

Dividing Equation (1) with Equation (2)

$\large{\boxed{\tt \dfrac{F_1}{F_2} = \dfrac{5x}{3x}}}$

Substituting the values,

$\longmapsto \large{\tt \dfrac{F_1}{F_2} = \dfrac{M_1 \times a_1}{M_2 \times a_2}}$

Substituting the values,

$\longmapsto \large{\tt \dfrac{5x}{3x} = \dfrac{3x \times a_1}{5x \times a_2}}$

$\longmapsto \large{\tt \cancel{\dfrac{5x}{3x}} = \dfrac{3x.a_1}{5x.a_2}}$

$\longmapsto \large{\tt \dfrac{5}{3} = \cancel{\dfrac{3x.a_1}{5x.a_2}}}$

$\longmapsto \large{\tt \dfrac{5}{3} = \dfrac{3 \times a_1}{5 \times a_2}}$

$\longmapsto \large{\tt \dfrac{5}{3} = \dfrac{3}{5} \times \dfrac{a_1}{a_2}}$

$\longmapsto \large{\tt \dfrac{3}{5} \times \dfrac{a_1}{a_2} = \dfrac{5}{3}}$

$\longmapsto \large{\tt \dfrac{a_1}{a_2} = \dfrac{5}{3} \times \dfrac{5}{3}}$

$\longmapsto \large{\tt \dfrac{a_1}{a_2} = \dfrac{25}{9}}$

$\large\longmapsto{\underline{\boxed{\red{\tt a_1 : a_2 = 25 : 9}}}}$

∴ The Ratios of Acceleration (a₁ : a₂) is 25 : 9.

$\rule{300}{1.5}$

Answer 2

Answer:

Given:

Mass of the objects are in the ratio of

3 : 5

Forces are in the ratio of 5 : 3

To find:

Ratio of Acceleration

Formulas used:

F = m × a ,

F => Force, m=> mass and a=> acceleration.

Calculation:

Let Force of 1st particle be F1 and that of 2nd particle be F2.

$\frac{F1}{F2} = \frac{5}{3}$

$= > \frac{m1 \times a1}{m2 \times a2} = \frac{5}{3}$

$= > ( \frac{m1}{m2} ) \times (\frac{a1}{a2} ) = \frac{5}{3}$

$= > \frac{3}{5} \times \frac{a1}{a2} = \frac{5}{3}$

$= > \frac{a1}{a2} = \frac{25}{9}$

So, ratio of acceleration = 25 : 9