A variable force F = (3x^2 + 2x) N acts on a particle. The work done by this force in moving the particle from x = 1 m to x = 2 m is: MCQ with Answer and Explanation
A variable force F = (3x^2 + 2x) N acts on a particle. The work done by this force in moving the particle from x = 1 m to x = 2 m is:
A. 14 J
B. 12 J
C. 10 J
D. 16 J
Answer: Option C
Solution (By JKSSB Mock Tests)
Work done by a variable force is the definite integral of F dx. W = Integral(3x^2 + 2x) dx from 1 to 2. W = [x^3 + x^2] evaluated from 1 to 2. Upper limit: (2^3 + 2^2) = 8 + 4 = 12. Lower limit: (1^3 + 1^2) = 1 + 1 = 2. Work = 12 - 2 = 10 Joules.
Explanation:
Boiling occurs when vapour pressure equals atmospheric pressure. At high altitude, atmospheric pressure is lower, so water boils at lower temperature. Pressure cooker increases pressure to raise boiling point for faster cooking.
Explanation:
Resistance R = rhoL/A. If the wire is stretched so length becomes L' = 2L, the volume (V = AL) must remain constant. Therefore, the new area A' must be A/2 to maintain V. The new resistance R' = rho(2L)/(A/2) = 4 * (rhoL/A) = 4R. Stretching a wire to double its length increases its resistance strictly by a factor of 4. This is a classic trap question compared to merely 'changing the wire'.
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