Question

A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion:
a. $Y = a sin 2p \frac{t}{T}$\
b. Y = a sin vt
c. $Y = (\frac{a}{T}) sin \frac{t}{a}$
d. $Y = (\frac{a}{\sqrt{2}}) (sin \frac{2\pi t}{T}+ cos \frac{2\pi t}{T})$
(a = maximum displacement of the particle, v = speed of the particle, T = time period of the particle motion)
Rule out the wrong formulas on dimensional grounds.

Answer 1

Hii there,

# Step-by-step solution-
- The displacement y has the dimension of length. i.e. [L]
- Therefore, the formula for it should also have the dimension of length.

Now, we'll derive dimensions one by one,
a. y = a.sin(2πt/T)
dimensions = [L]

b. y = a.sin(vt)
dimensions = [L]

c. y = a/T sin(t/a)
dimensions = [LT^-1]

d. y = a/√2 [sin(2πt/T)+cos(2πt/T)]
dimensions = [L]

As options (3) have different dimensions from displacement, that's a wrong formula.

Hope this helps you...

Answer 2

Answer:

Hlo mate here's your asnwer

Option b and c

hope it helps you

have a great day