The units of c are: [c] = m²/s³. The answer is b.
The given equation is a = cmv²sinθ/rt, where a is acceleration, m is mass, v is velocity, r is radius, t is time, θ is an angle, and c is a constant.
To determine the units of c, we can analyze the units of each term in the equation and then determine the units of c such that the units of the equation are consistent.
Units of each term in the equation are:
a: m/s²
m: kg
v: m/s
r: m
t: s
sinθ: dimensionless
Substituting these units in the given equation, we get:
[m/s²] = [c] x [kg] x [m/s]² x [dimensionless] / [m] x [s]
Simplifying the above equation, we get:
[c] = [m/s²] x [m] x [s] / [kg] x [m/s]² x [dimensionless]
Therefore, the units of c are:
[c] = m²/s³
Hence, option (b) m²/s³ could be the units of c.
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