Definition of distance -AR type problem

[Jahnavi]

Homework Statement

Homework Equations

The Attempt at a Solution

These assertion reasoning questions are little tricky . Even simple questions get wrong in a time bound objective test .

In this question I think it should be option b) i.e Both the statements are correct but Statement R is not the correct explanation of statement A . But this is marked wrong .

Statement R doesn't explain that a scalar quantity has only magnitude but no direction .Displacement is also length of the path along with the direction.

What option would other members choose ?

 

[palkia]

Dispacement is the vector not distance.It should be (c)

 

[Jahnavi]

Dispacement is the vector not distance.It should be (c)

No . c) is clearly wrong .

Please read the question carefully . R is correct statement .

@haruspex , what would you choose ?

I guess it's a toss up between a) and b) .

 

[haruspex]

Dispacement is the vector not distance.It should be (c)

That is in itself an example of (d).

 

[haruspex]

No . c) is clearly wrong .

Please read the question carefully . R is correct statement .

@haruspex , what would you choose ?

I guess it's a toss up between a) and b) .

The difficulty is that we are not provided a definition of length of path traversed. Here it is: If $\vec {ds}$ is the general vector element of a path P then length traversed is $\int_P|\vec {ds}|$
This is clearly a scalar, so (a).

 

[palkia]

Looks like I misread the question...my mistake.

I think it should be (A) then

 

[Jahnavi]

The difficulty is that we are not provided a definition of length of path traversed. Here it is: If $\vec {ds}$ is the general vector element of a path P then length traversed is $\int_P|\vec {ds}|$
This is clearly a scalar, so (a).

OK . I agree R is a correct statement

But the point is whether R is a correct reasoning for statement A .Does R correctly explain statement A ?

 

[haruspex]

OK . I agree R is a correct statement

But the point is whether R is a correct reasoning for statement A .Does R correctly explain statement A ?

In post #5 I provided the (missing) definition of length of path traversed. That definition clearly makes length of path traversed a scalar. The R statement claims that distance is length of path traversed, and you accept that as true. Does it not follow that distance is a scalar?

 

[Jahnavi]

Does it not follow that distance is a scalar?

OK .

Is it okay if I combine the two statements and read them together like this =>

Since/Because distance is the length of path traversed , it is a scalar quantity .

OR

Distance is a scalar quantity because it is the length of path traversed .

Is that correct ?

 

[haruspex]

OK .

Is it okay if I combine the two statements and read them together like this =>

Since/Because distance is the length of path traversed , it is a scalar quantity .

OR

Distance is a scalar quantity because it is the length of path traversed .

Is that correct ?

Yes, both forms are correct.

 

[Jahnavi]

Thanks

 

[Orodruin]

The difficulty is that we are not provided a definition of length of path traversed. Here it is: If $\vec {ds}$ is the general vector element of a path P then length traversed is $\int_P|\vec {ds}|$
This is clearly a scalar, so (a).

I disagree. The distance between two points is a scalar so the assertion is true. However, the distance between two points is independent of the path - it is the length of the shortest path - which makes the stated reason a false statement unless you specify that the path must be a straight line.

 

[haruspex]

I disagree. The distance between two points is a scalar so the assertion is true. However, the distance between two points is independent of the path - it is the length of the shortest path - which makes the stated reason a false statement unless you specify that the path must be a straight line.

Yes and no.
The question takes "distance" out of context. It is not clear whether we are discussing distance between two points or distance traveled. Since it mentions a path traversed, I feel it is reasonable to assume that context.
So to be precise, distance can mean the length of path traversed, and when it does mean that it follows that it is a scalar.