Question 140: Units , Dimensions and Error Analysis

Question

The force is given in terms of time t and displacement x by the equation
F = A cos Bx + C sin Dt
The dimensional formula of $${{AD} \over B}$$ is :

Accepted Answer

$$[A] = [ML{T^{ - 2}}]$$
$$[B] = [{L^{ - 1}}]$$
$$[D] = [{T^{ - 1}}]$$
$$\left[ {{{AD} \over B}} \right] = {{[ML{T^{ - 2}}][{T^{ - 1}}]} \over {[{L^{ - 1}}]}}$$
$$\left[ {{{AD} \over B}} \right] = [M{L^2}{T^{ - 3}}]$$

Answer

$$[{M^0}L{T^{ - 1}}]$$

Answer

$$[M{L^2}{T^{ - 3}}]$$

Answer

$$[{M^1}{L^1}{T^{ - 2}}]$$

Answer

$$[{M^2}{L^2}{T^{ - 3}}]$$

Units , Dimensions and Error Analysis

The force is given in terms of time t and displacement x by the equation F = A cos Bx + C sin Dt The dimensional formula of ${{AD} \over B}$ is :

Choose the correct answer: