Question

Suppose a force is given by the expression=kx²;where x has the dimension of length.The dimension of k is:

• A. ML^-1T^-1
• B. MLT^-1
• C. MLT^-2
• D. M^-1L^-1T
• E. ML^-1T^-2

Answer 1

Answer: (E)

Given:

• Force expression: \( F = kx^2 \)
• \( x \) has the dimension of length (\( \text{L} \))

Step 1: Write the Dimensional Formula for Force

Force has the dimensional formula:

\[ [F] = \text{M L T}^{-2} \]

Step 2: Express the Dimensional Formula for \( k \)

From \( F = kx^2 \), we can solve for \( k \):

\[ k = \frac{F}{x^2} \]

Substitute the dimensions:

\[ [k] = \frac{[F]}{[x^2]} = \frac{\text{M L T}^{-2}}{\text{L}^2} = \text{M L}^{-1} T^{-2} \]

Conclusion:

The dimension of \( k \) is \( \text{M L}^{-1} T^{-2} \).

Answer: \(\boxed{E}\)

Answer 2

Force = \(kx^2\)

Dimension of Force (F) = \(MLT^{-2}\)

Dimension of x = \(L\)

Dimension of \(x^2\) = \(L^2\)

Therefore, the dimension of k can be found as follows:

\([MLT^{-2}] = k[L^2]\)

\(k = \frac{[MLT^{-2}]}{[L^2]}\)

\(k = [ML^{-1}T^{-2}]\)

Final Answer: The final answer is \(\boxed{E}\)