Solution - Career Point

6.[A]I 2f–f sin60º f cos60º +fI 1xu = -f cos60ºf = +f1 1 1= −f v − f cos 60º1 1 2= +f v f1 2 1− =f f vv = -ff = cos 60ºxf= xcos 60ºx = 2f∴ final image will formed at optical centre of firstlens.7.[C] C v = (3 + 2T)RdQ = dU + PdVadiabatic process dQ = 00 = Rn (3 + 2T)dT + PdVnRT0 = Rn(3 + 2T)dT + dVVdV ⎛ 3 + 2T ⎞∫−= ∫⎜⎟dTV ⎝ T ⎠– log V = 3 logT + 2T + C– logV – logT 3 = 2T + Clog VT 3 = 2T + CVT 3 = e 2TVT 3 e -2T = C8.[A] P = P 0 − αVPV = RTRT2= P 0 − αVV3P0 V αVT = −R RdT = 0dV2P03αV− =R R0PV = 03 α2Now put V in T.• Saturn’s rings are made up of particles of ice, dustand rock. Some particles are as small as grains ofsand while others are much larger thanskyscrapers.• Jupiter is larger than 1,000 Earths.• The Great Red Spot on Jupiter is a hurricane-likestorm system that was first detected in the early1600’s.• Comet Hale-Bopp is putting out approximately250 tons of gas and dust per second. This isabout 50 times more than most comets produce.• The Sun looks 1600 times fainter from Pluto thanit does from the Earth.• There is a supermassive black hole right in themiddle of the Milky Way galaxy that is 4 milliontimes the mass of the Sun.• Halley’s Comet appears about every 76 years.• The orbits of most asteroids lie partially betweenthe orbits of Mars and Jupiter.• Asteroids and comets are believed to be ancientremnants of the formation of our Solar System(More than 4 billion years ago!).• Comets are bodies of ice, rock and organiccompounds that can be several miles in diameter.• The most dangerous asteroids, those capable ofcausing major regional or global disasters, usuallyimpact the Earth only once every 100,000 yearson average.• Some large asteroids even have their own moon.• Near-Earth asteriods have orbits that cross theEarth’s orbit. These could potentially impact theEarth.• There are over 20 million observable meteorsper day.• Only one or two meteorites per day reach thesurface of Earth.• The largest found meteorite was found in Hoba,Namibia. It weighed 60 tons.XtraEdge for IIT-JEE 19 APRIL 2010