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Question: 1. The displacement x of a particle at time t moving under a constant force is in meters, t in seconds. Find the work done by the force in the interval from t = 0 to t = 6 second.
Ans:
v at t = 0, – 6 m/s
v at t = 6 sec., 6 m/s
change in KE is zero ⇒ work done = 0
Question: 2. Calculate the distance above and below the surface of the earth at which the acceleration due to gravity is the same
Ans:
on solving we get
– Rh + R^{2} – h^{2} = 0
Question: 3. A ray of light travelling inside a rectangular glass block of refractive index √2 is incident on the glassair surface at an angle of incidence of 45°. Show that the ray will emerge into the air at an angle of refraction equal to 90°
Ans: Given C = 45°
So the ray will graze the interface after refraction at an angle of 90°
Question: 4. Two cells each of same e.m.f ‘e’ but of internal resistances r^{1} and r^{2 }are connected in series through an external resistance R. If the potential difference between the ends of the first cell is zero, what will be the value of R in terms r^{1 }and r^{2} ?
Ans:
Question: 5. At time t = 0, a radioactive sample has a mass of 10 gm. Calculate the expected mass of radioactive sample after two successive mean lives.
Ans:
Two successive mean lives =
No. of nuclei after two mean lives =
Therefore mass =
Question: 6. Calculate the number of H+ ion present in 1 ml of a solution whose pH is 10.
Ans: pH = 10
[H^{+}] = 10^{–10 }M
In 1000 ml solution there are 6.023 × 10^{13} H^{+} ions
In 1 ml solution there are 6.023 × 10^{10} H^{+} ions
Question: 7. Give the structure of pyrosulfuric acid. How would you prepare it? What would you observe when colourless HI is added to pyrosulfuric acid?
Ans:
Question: 8. Write with a balanced chemical equation how gypsum is used for the conversion of ammonia into ammonium sulfate without using H_{2} SO_{4} .
Ans: Balanced reaction is
2NH_{3} + CaSO_{4} + CO_{2} + H_{2}O = (NH_{4 })_{2 }SO_{4} + CaCO_{3}
Question: 9. Convert phenol to phydroxy acetophenone in not more than 2 steps.
Ans:
Question: 10. An organic compound ‘A’ on treatment with ammoniacal silver nitrate gives metallic silver and produces a yellow crystalline precipitate of molecular formula C_{9}H_{10}N_{4}O_{4 }, on treatment with Brady’s reagent. Give the structure of the organic compound ‘A’.
Ans: Compound (A) is an aldehyde. It should be propanal CH_{3}CH_{2}CHO
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