61. Two spherical nuclei of radii and have respectively mass numbers 216 and 64. The ratio is:
(a) 0.75
(b) 1.0
(c) 1.3
(d) 3.375
Answer:
(c) 1.5
Explanation:
The nuclear radius is proportional to the cube root of the mass number (). Therefore, . (Note: The exam source text registers option c as 1.3 due to an OCR/typo error, but the mathematical solution is indeed 1.5).
62. The potential energy U, of two atoms in a solid separated by a distance x is given by , where A is a positive constant. The force exerted by one atom on the other is :
(a)
(b)
(c)
(d)
Answer:
(c)
Explanation:
Force is the negative spatial derivative of potential energy: .
63. If the two inputs of a NAND gate are shorted, the gate will be equivalent to:
(a) OR
(b) XOR
(c) NOR
(d) NOT
Answer:
(d) NOT
Explanation:
Shorting the two inputs of a NAND gate means both inputs receive the exact same logic signal (A). The output becomes , which simplifies by Boolean algebra to , functioning as a NOT gate.
64. The percentage errors in the measurement of mass and speed are 2% and 3%, respectively. How much will be the maximum errors in the estimate of kinetic energy obtained by measuring mass and speed ?
(a) 8%
(b) 7%
(c) 9%
(d) 6%
Answer:
(a) 8%
Explanation:
Kinetic energy . The relative percentage error is calculated by adding the percentage error in mass to twice the percentage error in velocity: .
65. Let the dimensions of mass, length, time and charge be $M^1$, $L^1$, $T^1$, and $C^1$, respectively. The dimensions of the magnetic induction field in terms of , , , will be :
(a)
(b)
(c)
(d)
Answer:
(a) $M^1 L^0 T^{-1} C^{-1}$
Explanation:
From the Lorentz force equation , we isolate . Applying dimensional analysis: .