Question

Example 2.16 The SI unit of energy is
J = kg m?s?: that of speed vis ms and
of acceleration a is ms. Which of the
formulae for kinetic energy (K) given below
can you rule out on the basis of
dimensional arguments (m stands for the
mass of the body):
(a) K = m v
(b) K = (1/2)mu
(c) K= ma
(d) K= (3/16)mu
(e) K = (1/2)mu? + ma​

Answer 1

Answer:

Dimensional analysis: Kinetic energy is [ML^2T^-2]

Explanation:

Answer 2

Answer:

Dimension of K.E = [M¹L²T-²]

• Dimension of equation a = [M²L³T-³]
• Dimension of equation b = [M¹L²T-²]
• Dimension of equation c = [M¹L¹T-²]
• Dimension of equation d = [M¹L²T-²]
• Dimension of equation e = DOESN'T HAVE PROPER DIMENSION. SINCE, TWO QUANTITIES OF DIFFERENT DIMENSIONS HAVE BEEN ADDED

K= (½)mv² is the correct formula for K.E

LHS= [M¹L²T-²] RHS=[M¹L²T-²]

LHS=RHS

THEREFORE, EQUATION B IS CORRECT FORMULA FOR K.E