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FUNDAMENTAL OF PHYSICS, Page 1 of 32, for IIT-JEE, NEET, 11th & 12th, Q1. Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube,, each of uniform mass density. Does the centre of mass of a body necessarily lie inside the, body?, Solution:, FOP, The study of nat, All the given structures are symmetric bodies having a very uniform mass density. Thus, for all the, above bodies their center of mass will lie in their geometric centres., R.K Sharma, It is not always necessary for a body's center of mass to lie inside it, for example, the, a circular ring is at its center., enter of mass of, Q2. In the HCI molecule, the separation between the nuclei of the two atoms is about 1.27 À (1 Å, = 1010 m). Find the approximate location of the CM of the molecule, given that a chlorine atom is, about 35.5 times as massive as a hydrogen atom and nearly all the mass of an atom is, concentrated in its nucleus., Solution:, OF P SICS., H, CI, Given,, drogen atom = 1 unit, chlorine atom = 35.5 unit, NDAMENTA, ( As a chlorine atom is 35.5 times the size ), Let the center of mass lie at a distance, from the chl, ne atom, Thus, the distance of center of mass from the hydrogen atom = 1.27 – x, Assuming that the center of mass of HCL lies at the origin,, Hydrogen will lie on the left side of the origin and chlorine lie on the right side of the origin, x = (-m (1.27 -x) + 35.5mx)/(m + 35.5m) = 0, -m (1.27 – x) + 35.5mx = 0, for IIT-JEE, NEET, 11th & 12th, R.K.Sharma (8507152734)

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The study of nature, Page 2 of 32, FUNDAMENTAL OF PHYSICS, for IIT-JEE, NEET, 11th & 12th, -1.27+x+35.5x 0, 36.5x = 1.27, IT-JEE, NEET., Therefore, x = (1.27)/36.5, 11th, 12th A, FOP, = 0.035 Å, The center of mass lies at 0.035 Å from the chlorine atom., R.K Sharma, Q3. A child sits stationary at one end of a long trolley moving uniformly with a speed V on a, smooth horizontal floor. If the child gets up and runs about on the trolley in any manner, what is, the speed of the CM of the (trolley + child) system?, Solution:, The child and the trolley constitute a single system and the child moving inside the trolley is a purely, internal motion. Since there is no external force on the system the, system will not change., elocity of the center of mass of the, Q4. Show that the area of the triangle contained between the vectors a and b is one half of the, magnitude of a x b, Solution:, E, A, The side AD is equal to a and AB is equal to b, Considering AADN :, sine = DN/AD = DN/ a, for IIT-JEE, NEET, 11th & 12th, R.K.Sharma (8507152734), NDAM, FUNDAMENTAL OF AYSCS, to

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The study of nature, Page 3 of 32, FUNDAMENTAL OF PHYSICS, for IIT-JEE, NEET, 11th & 12th, DN = a sine, Now, by definition a x, FOR, sine, = AB x DN, = (1/2) x [2 x AB x DN] (since area of the triangle ADB = 2x AB x DN], = (1/2) x la x, Sharma, Thus, area of AADB = x d x b, Q5. Show that a.(b x c) is equal in magnitude to the volume of the parallelepiped formed on the, three vectors, a, b and c., Solution:, Let the parallelepiped formed be:, K, Here,, ỞJ = à, ỞL = b and OK, %3D, n is a unit vector along OJ perpendicular to the plane containing b and &, for IIT-JEE, NEET, 11th & 12th, R.K.Sharma (8507152734), IN, to, FUNDANENAL OE PHYS