1
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

A man of mass $m$ starts falling towards a planet of mass $$M$$ and radius $$R$$. As he reaches near to the surface, he realizes that will pass through a small role in the planet. As he enters the role, we sees that the planet is really made of two pieces a spherical shell of negligible thickness of mass $$3 M / 4$$ and a point mass $$M / 4$$ at the centre. Change in the force of gravity experienced by the man is

A
$$\frac{3}{4} \frac{G M m}{R^2}$$
B
0
C
$$\frac{1}{3} \frac{G M m}{R^2}$$
D
$$\frac{4}{3} \frac{G M m}{R^2}$$
2
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

A vessel containing 1 mole of $$\mathrm{O}_2$$ gas (molar mass 32) at temperature $$T$$. The pressure of the gas is $$p$$. An identical vessel containing one mole of He gas (molar mass 4) at temperature $$4 T$$ has a pressure of

A
p/8
B
p
C
4p
D
8p
3
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

The fundamental frequency of an open organ pipe is $$600 \mathrm{~Hz}$$. The first overtone of this pipe has same frequency as first overtone of a closed organ pipe. If speed of sound is $$330 \mathrm{~m} / \mathrm{s}$$, then the length of a closed organ pipe is

A
21 cm
B
37 cm
C
31 cm
D
80 cm
4
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

A Carnot's heat engine works between the temperature $$527^{\circ} \mathrm{C}$$ and $$127^{\circ} \mathrm{C}$$. What amount of heat should it consume per second to deliver mechanical work at the rate of $$1.0 \mathrm{~kW}$$ ?

A
0.477 kcal/s
B
4.77 kcal/s
C
447.7 kcal/s
D
0.2385 kcal/s
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