Acceleration of Block B

Given:
Mass of Block A (mA) = 2m
Mass of Block B (mB) = m
Force applied on Block A (F) = 5mg
Acceleration of Block B (aB) = g

To find:
Acceleration of Block A (aA)

Using Newton's second law of motion, we can relate the force, mass, and acceleration of an object:

Force (F) = mass (m) × acceleration (a)

Since the force is applied on Block A, we can write the equation as:

5mg = 2m × aA [Equation 1]

Since Block A and Block B are connected by a spring, they will experience the same acceleration, denoted as a. Therefore, we can write the equation for Block B as:

m × g = m × a [Equation 2]

Simplifying Equation 2, we find that the acceleration of Block B is equal to the acceleration due to gravity (g).

Now, let's solve for the acceleration of Block A using Equation 1:

5mg = 2m × aA

Simplifying the equation, we find:

aA = 5g/2

Therefore, the acceleration of Block A at that instant is 5g/2.

Explanation:

- We have two blocks, A and B, connected by a spring.
- A horizontal force of 5mg is applied to Block A.
- The mass of Block A is 2m, and the mass of Block B is m.
- The acceleration of Block B at that instant is g.
- To find the acceleration of Block A, we can use Newton's second law of motion.
- According to the law, the force applied on an object is equal to the mass of the object multiplied by its acceleration.
- By applying this law to Block A, we can write an equation relating the force, mass, and acceleration of Block A.
- Since Block A and Block B are connected by a spring, they will experience the same acceleration.
- By equating the force, mass, and acceleration of Block B, we can find that the acceleration of Block B is equal to the acceleration due to gravity (g).
- Substituting the values into the equation for Block A, we can solve for the acceleration of Block A.
- Simplifying the equation, we find that the acceleration of Block A at that instant is 5g/2.

Is it 2g ?