Magnitude of force F experienced by a certain object moving with speed v is given by F=Kv race to 2, where K is constant. Find the dimension of K

MT⁻¹

Given equation:

F = Kv        (i)

Where;

F = Magnitude of force experienced by the object

v = speed at which the object is moving

K = constant.

To get the dimension of K, follow the following steps:

i. Make K subject of the formula in equation(i)

K = F / v

ii. Get the dimension of force F and speed v

Dimension of force = MLT⁻²

Dimension of velocity = LT⁻¹

iii. Substitute these dimensions into the result of (i) above;

K = MLT⁻² / LT⁻¹

iv. Simplify the result in (iii)

First, the Ls in the numerator and denominator will cancel out

K = MT⁻² / T⁻¹

Next, the Ts will be expressed as follows

K = MT⁻² x T¹           [using the law of indices]

K = MT⁻²⁺¹

K = MT⁻¹

Therefore, the dimension of K is MT⁻¹

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