At what temperature do the Fahrenheit and celcius scales give the same reading?
Answer: C
The two scales read alike at −40°.
Setting the readings equal in the conversion formula: \[F = \frac{9}{5}C + 32,\qquad x = \frac{9}{5}x + 32\]
\[-\frac{4}{5}x = 32 \Rightarrow x = -40\]
So −40 °C is the same temperature as −40 °F.
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Two bodies A and B are of same mass and same amount of heat is given to both of them. If the temperature of A increases more than that of B because of heat addition, then
Answer: B
The specific heat capacity of A is less than that of B.
From \[Q = mc\,\Delta T \Rightarrow \Delta T = \frac{Q}{mc}\] the same heat given to the same mass produces a larger temperature rise where \(c\) is smaller. A heats up more, so its specific heat capacity is the lower.
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Which of the following is a vector quantity
Answer: A
Momentum is a vector.
It is mass times velocity, and velocity has direction, so momentum points the same way. Pressure, energy and work are all scalars - work is a dot product of two vectors, which yields a scalar.
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What are the particles emitted by a radioactive element after three consecutive disintegrations that leave it in the same group of the periodic table?
Answer: C
The particles are one alpha and two beta.
An alpha emission lowers the atomic number by 2 and a beta emission raises it by 1: \[Z \rightarrow Z-2+1+1 = Z\] So the nucleus returns to the same group of the periodic table, though its mass number has fallen by 4 - the daughter is an isotope of the original element.
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Pick out the only vector quantity
Answer: B
Impulse is the vector quantity.
It is force multiplied by time, and force has direction, so impulse does too - it equals the change in momentum. Pressure, gravitational potential and the coefficient of friction are all scalars.
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Heat is associated with
Answer: A
Heat is associated with the kinetic energy of the random motion of molecules.
Temperature measures the average of that random kinetic energy. Orderly motion of the whole body is not heat but bulk kinetic energy: a moving cricket ball is not hotter for moving.
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The earliest thermometer was developed by
Answer: D
The earliest thermometer was developed by Galileo.
His thermoscope of about 1593 used the expansion and contraction of air in a bulb to move a column of water. It had no fixed scale, so it showed changes in temperature without measuring them; Fahrenheit's mercury thermometer with a scale came in 1714.
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What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R at the bottom so that it can complete the loop?
Answer: D
The minimum entry speed is \(\sqrt{5gR}\).
At the top of the loop, gravity must at least supply the centripetal force: \[mg = \frac{mv_{top}^2}{R} \Rightarrow v_{top}^2 = gR\]
Applying conservation of energy between bottom and top, a height \(2R\) apart: \[\tfrac{1}{2}mv^2 = \tfrac{1}{2}mv_{top}^2 + mg(2R)\]
\[v^2 = gR + 4gR = 5gR \Rightarrow v = \sqrt{5gR}\]
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A parsec is the unit of
Answer: A
A parsec is a unit of distance.
It is the distance at which one astronomical unit subtends an angle of one arcsecond - the name is short for parallax-second. One parsec is about \(3.26\) light years, or \(3.086\times10^{16}\) m.
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A capillary tube is partially dipped vertically in a vessel containing water. Due to capillarity water rises in the tube. The height of water rise in the tube can be increased by
Answer: A
The rise is increased by decreasing the radius of the tube.
The height of capillary rise is \[h = \frac{2T\cos\theta}{r\rho g}\] so \(h\) varies inversely with the radius. The height of water already in the vessel does not enter the formula at all.
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