The acceleration a of an object is given by the equation a=a+bt+ct^3 where t refers to time. (a) what are the dimensions of a, b, and c? (b) what are the si units for the constants a, b, and c?

(a) A =

B =

(b) A =

B =

C =

Solution:

The acceleration of a body is the rate at which the velocity of the body changes.

Thus

The SI unit of velocity of an object is and its dimension is [LT^{- 1}] and for time, T the SI unit is second, s and dimension is [T] and hence

The SI unit and dimension for the acceleration of an object is and [LT^{- 2}] respectively.

Now, as per the question:

acceleration, a =

(a) Now, according to the homogeneity principle in dimension, the dimensions on both the sides of the eqn must be equal,

For the above eqn:

Thus the dimensions of :

A =

BT =  

Thus for B

B =

(b) For the units of A, B and C, we will make use of their respective dimensional formula from part (a)

where

L corresponds to length in meter(m)

T corresponds to time in seconds(s)

Now, for:

A =

B =

C =

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards

there are no atoms