A cylinder of mass m rolls down an inclined plane from a height h above a horizontal level. If the velocity of the axis of the cylinder is v when it reaches the lower level, then
- A.v = gh
- B.v = mgh
- C.v = √(2gh)
- D.v < √(2gh)
Correct answer
Explanation
The correct answer is D, the speed is less than the square root of 2gh. A body that slides down a smooth slope turns all of its potential energy mgh into translational kinetic energy and reaches the bottom with a speed equal to the square root of 2gh. A cylinder that rolls without slipping must also spin, so the same mgh has to be shared between translation and rotation, and the speed of its axis is bound to come out smaller. Working it out for a solid cylinder, mgh equals half m v squared plus one fourth m v squared, which gives v as the square root of four gh by three, about 1.15 times the square root of gh against 1.41 for the sliding body. Option A is wrong because gh is not even a speed, as the units do not match. Option B is wrong because mgh is an energy and the mass cancels out in any case. Option C is wrong because that value belongs to a body that slides without rotating. Exam tip: of bodies rolling down the same slope, a solid sphere beats a solid cylinder, which beats a ring.
Practice Questions
View allThe fact that the planets move around the Sun, not in circles but in ellipses, was first demonstrated by
- A.Galileo
- B.Martin Luther
- C.Johannes Kepler
- D.Copernicus
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In 1609 Kepler showed that the planets move around the Sun in elliptical orbits, with the Sun at one focus of the ellipse.
Read the full explanation →Which one of the following statements is correct?
- A.Urea is produced in liver.
- B.Urea is produced in blood.
- C.Urea is produced from digestion of starch.
- D.Urea is produced in lung and kidney.
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Read the full explanation →Which one of the following is the correct sequence of passage of light in a compound microscope?
- A.Condenser-Objective lens-Eyepiece-Body tube
- B.Objective lens-Condenser-Body tube-Eyepiece
- C.Condenser-Objective lens-Body tube-Eyepiece
- D.Eyepiece-Objective lens-Body tube-Mirror
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Light passes through the condenser to the specimen, is picked up by the objective lens, travels up the body tube and reaches the eye through the eyepiece.
Read the full explanation →Which one of the following statements regarding haemoglobin is correct?
- A.Haemoglobin present in RBC can carry only oxygen but not carbon dioxide.
- B.Haemoglobin of RBC can carry both oxygen and carbon dioxide.
- C.Haemoglobin of RBC can carry only carbon dioxide.
- D.Haemoglobin is only used for blood clotting and not for carrying gases.
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Read the full explanation →Which one of the following statements regarding histone proteins is correct?
- A.Histones are proteins that are present in mitochondrial membrane.
- B.Histones are proteins that are present in nucleus in association with DNA.
- C.Histones are proteins associated with lipids in the cytosol.
- D.Histones are proteins associated with carbohydrates in the cytosol.
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They are the proteins around which DNA winds to form chromatin in the nucleus of eukaryotic cells. Histones are small basic proteins, rich in the positively charged amino acids lysine and arginine, which attract the negatively charged phosphate groups of DNA.
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