Question

check whether the equation. T=2π √m/g is dimensionally correct. T----> time period of a simple pendulum. m-----> mass of the bob. g------> acceleration due to gravity.

Answer 1

Let Time period =T

     Mass of the bob = m

     Acceleration due to gravity = g

    Length of string = L

Let

⇒a=0 ⇒ Time period of oscillation is independent of mass of the bob

-2b=1

⇒b=-

b+c = 0

1/2 + c =0

c= ½

Giving values to a,b and c in first equation T proportional m * g^-1/2 L^1/2 T proportional to root L/g

The real expression for Time period is    T = 2 Pie root L/g

Therefore time period of oscillation depends only on gravity and length of the string.

Not on mass of the bob.

Answer 2

Answer:

The oscillation depends on gravity and length of string not mass

Explanation:

Time=t

Mass=m

Gravity=g

Length=L

let a=0

-2b=1b

b=-1

1\2+C=0

C=1\2

Therefore time period ,T =2¶√l\g

Hence proved