Question

Denote the speeds of block at point a and a' (the same point for different two cases) to be va and va' respectively. What is the ratio of the speeds va/va'? 1. va/va' = 1/4 2. va/va' = 4 3. va/va' = 1/3 4. va/va' = 1/5 5. va/va' = 2 6. va/va' = 1/2 7. va/va' = ?

1) 1/4
2) 4
3) 1/3
4) 1/5
5) 2
6) 1/2
7) ?

Answer 1

The ratio of the speeds is
`\[ (va)/(va') = (1)/(4) \]`.

Step-by-step explanation:

The correct answer is
`\( (va)/(va') = (1)/(4) \)`. To understand this, let's denote the speeds at points a and a' as
`\( v_a \)` and \( v_{a'} \) respectively. The ratio
`\( (va)/(va') \)` is a representation of the change in speed between the two points. In this case, the given ratio
`\( (1)/(4) \)` implies that the speed at point a is one-fourth of the speed at point a'.

Now, if we express this mathematically,
`\( (va)/(va') = (1)/(4) \)`means that the speed at point a (( va \)) is one-fourth of the speed at point a' (\( va' \)). This ratio helps us understand the relationship between the speeds at the two points. It indicates that the speed at point a is significantly less than the speed at point a'.

In conclusion, the correct choice is
`\( (va)/(va') = (1)/(4) \)`, signifying that the speed at point a is a quarter of the speed at point a'. Understanding such ratios is fundamental in analyzing the dynamics of motion and velocity changes at different points in a system.