Question

A force produces an acceleration of 2 metre per second square in a body A and 5 metre per second square in another body B find the ratio of the mass ofA to the mass of B

Answer 1

Answer:

5/2

Step-by-step explanation:

F=ma

a¹=2m/s²

m¹=F/2 kg

m²=F/5kg

then m¹/m²= F/2/F/5

=5/2

Answer 2

Given,

A force produces acceleration:

2 m/s² in body A, and,

5 m/s² in body B.

To find,

The ratio of the mass of body A to that of B.

Solution,

Firstly, the relation between the acceleration due to a force on a body is given by Newton's second law of motion. According to this law,

$F = ma$     ...(1)

Where,

F = force applied (N),

m = mass of the body (m),

a = acceleration (m/s²)

Let body A be represented by subscript a, and body B by subscript b.

The force applied is given to be the same for both A and B. Let the force be F.

Now, for body A using equation (1), we have,

$F=(m_a)\cdot (a_a)$

⇒ $F=m_a(2)$

⇒ $F=2m_a$     ...(2)

For body B, from equation (1),

$F=(m_b)\cdot (a_b)$

⇒ $F=(m_b) (5)$

⇒ $F=5m_b$     ...(3)

To obtain the required ratio, that is $m_a:m_b$, we can simply equate, or divide the equation (2) by (3).

So,

$\frac{F}{F} =\frac{2m_a}{5m_b}$

Rearranging and simplifying,

$\frac{m_a}{m_b}=\frac{5}{2}$

Or,

$m_a:m_b=5:2$

Therefore, the ratio of the mass of body A to that of B will be 5:2.