Question

The displacement of a particle is given by s = at + bt2 where t is time and ‘a’ and ‘b’ are two constants. The dimensional formula of the constant b is (A) M0 L 0 T 2 (B) M0 L 1 T 0 (C) M0 L 1 T –2 (D) M0 L 0 T 1

Answer 1

Explanation:

A=[L/T ]

B=[L/T^2]

As both the term has same unit as of s in LHS

Answer 2

Answer:

The correct answer is Option C i.e. $M^{0} L^{1} T^{-2}$.

Explanation:

The dimensional formula of s is $M^{0} L^{1} T^{0}.$

The dimensional formula of $t^{2}$ is $M^{0} L^{0} T^{2}.$

In a physical expression, the dimensional formulas of all units is same.

Hence, dimensional formula of b$t^{2}$ is same as of s.

Hence,

$M^{0} L^{1} T^{0}$ = b x $M^{0} L^{0} T^{2}$

b = $\frac{M^{0} L^{1} T^{0}}{M^{0} L^{0} T^{2}}$

b = $M^{0} L^{1} T^{-2}$

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