Question

1. The displacement of a particle S is given by S=A+Bt+Ct². Deduce the units of the constants A, B and C.

2. The force of capillarity in plant is given by r=prgh/2 where r is the coefficeint of surface tension. Is the equation correct or not? Justify the Answer

3. Given the vander waal's equation of state as (p+q/v²)(v-b)=RT.

Answer 1

1.

$$\dim{S}=\dim{(A+Bt+Ct^2)}$$

$$[A]=[S]=m$$

$$[B]=\frac{[S]}{[t]}=\frac{m}{s}$$

$$[C]=\frac{[S]}{[t]^2}=\frac{m}{s^2}$$

2.

$$F=0.5prgh$$

$$\dim F=MLT^{-2}$$

$$\dim g=LT^{-2}$$

$$\dim h=L$$

$$\dim r=MT^{-2}$$

$$\dim p=ML^{-1}T^{-2}$$

Thus,

$$\dim(0.5prgh)=M^2LT^{-6}$$

It is not equal the dimension of force. Therefore, the formula is not correct!