The force is given in terms of time t and displacement x by the equation F = A cosBx + C sin DtThe dimensional formula of is (a) [M 0 LT− 1] (b) [M L2T− 3] (c) [M 1 L1T−2] [M2 L2T−3]
Question
The force is given in terms of time t and displacement x by the equation F = A cosBx + C sin DtThe dimensional formula of is (a) [M 0 LT− 1] (b) [M L2T− 3] (c) [M 1 L1T−2] [M2 L2T−3]
Solution
The dimensional formula of a physical quantity is a representation of the fundamental dimensions (such as mass, length, time, etc.) that make up the quantity. In the given equation, F = A cosBx + C sin Dt, F represents force.
The dimensional formula of force (F) is [M^1 L^1 T^-2], where M represents mass, L represents length, and T represents time. This is because force is a derived quantity in physics, calculated as the product of mass (which has a dimension of M^1) and acceleration (which has a dimension of L^1 T^-2).
Therefore, the correct answer is (c) [M^1 L^1 T^-2].
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