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Standard XII

Physics

Relating Circular Motion to SHM

The velocity ...

Question

The velocity v of a particle at time t is given by v=at+ b/t+ c where a,b,c are constants . What will be the dimensions of a,b and c

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Solution

we follow the rule : when we add or subtract some terms, all these terms should be of the same dimensions to which they are equated.
so, [at] = [v]
[a] [T] = [LT^-1]
[a] = [LT^-2]
and, [b/t] = [v]
[b] [T^-1] = [LT^-1]
[b] = [L]
also, [c] = [v]
[c] = [LT^-1]

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The velocity v of a particle at time t is given by v=at+ b/t+ c where a,b,c are constants . What will be the dimensions of a,b and c

we follow the rule : when we add or subtract some terms, all these terms should be of the same dimensions to which they are equated.so, [at] = [v][a] [T] = [LT-1][a] = [LT-2]and, [b/t] = [v][b] [T-1] = [LT-1][b] = [L]also, [c] = [v][c] = [LT-1]

we follow the rule : when we add or subtract some terms, all these terms should be of the same dimensions to which they are equated.
so, [at] = [v]
[a] [T] = [LT^-1]
[a] = [LT^-2]
and, [b/t] = [v]
[b] [T^-1] = [LT^-1]
[b] = [L]
also, [c] = [v]
[c] = [LT^-1]