Question

the velocity of a body is given by equation v=a+bx where x is displacement.the unit of b is

Answer 1

The velocity of a body is given by equation, v = a + bx , where x is displacement.

we have to find unit of b.

from dimensional analysis,

dimension of v = dimension of {a + bx}

= dimension of a + dimension of bx

= dimension of bx

= dimension of b × dimension of x

we know, dimension of v = [LT-¹]

and dimension of x = [L]

so, [LT-¹] = dimension of b × [L]

or, [T-¹] = dimension of b

hence, dimension of b = [T-¹]

so, unit of b = sec^-1 or cycle per second.

[ know more : but we know, cycle per second is the unit of frequency.so, we can say that unit of b is equal or unit of frequency. ]