Tiêu đề 02A.GRAVITATION (57 - 75).pdf ✅

Jr Chemistry E/M GRAVITATION 5 8 NISHITH Multimedia India (Pvt.) Ltd., JEE - ADVANCED - VOL-III NISHITH Multimedia India (Pvt.) Ltd., 6. The following figure shows two shells of masses m1 and m2 . The shells are concen- tric. At which point, a particle of mass m shall experience zero force? m1 m2  D C B A A) A B) B C) C D) D 7. Consider two solid uniform spherical objects of the same density  . One has radius R and the other has radius 2R . They are in outer space where the gravitational fields from other objects are negligible. If they are arranged with their surface touching, what is the contact force between the objects due to their gravitational attraction? A) 2 4 G R  B) 128 2 4 2 81 G R   C) 128 2 81 G D) 128 2 2 87  R G 8. A thin rod of length L is bent to form a circle. Its mass is M . What force will act on the mass m placed at the centre of the circle? A) 2 2 4 GMm L  B) 2 2 4 GMm  L C) 2 2 GMm L  D) zero 9. Three particles each of mass M are placed at the three corners of an equilateral triangle of side l . What is the force due to this sys- tem of particles on another particle of mass m placed at the midpoint of any side? A) 2 3 4 GMm l B) 2 4 3 GMm l C) 2 4 GMm l D) 2 4GMm l 10. A solid sphere of uniform density and mass M has radius 4m . Its centre is at the origin of the coordinate system. Two spheres of radii 1 m are taken out so that their centres at P0, 2,0   and Q0,2,0 respectively. This leaves two spherical cavities. What is the gravitational field at the origin of the co- ordinate axes?    P O Q Y Z X A) 31 1024 GM B) 1024 Gm C) 31GM D) zero 11. Gravitational field at the centre of a semi- circle formed by a thin wire AB of mass m and length l is O y A B x l A) 2 Gm l along x axis B) 2 Gm l along y axis C) 2 2 Gm l  along x axis D) 2 2 Gm l  along y axis
NISHITH Multimedia India (Pvt.) Ltd., 5 9 GRAVITATION NISHITH Multimedia India (Pvt.) Ltd., JEE - ADVANCED - VOL-III 12. Four similar particles of mass m are orbit- ing in a circle of radius r in the same angu- lar direction because of their mutual gravi- tational attractive forces. Velocity of a par- ticle is given by      r m m m m A) 1 2 1 2 2 4 Gm r                B) 3 Gm r C) 1 2 2  Gm r  D) 1 2 1 1 2 2 2 2 Gm r              13. The gravitational potential due to earth at infinite distance from it is zero. Let the gravi- tational potential at a point P be 1 5 J kg   . Suppose, we arbitrarily assume the gravita- tional potential at infinity to be 1 10 J kg   , then the gravitational potential at P will be A) 1 5 J kg   B) 1 5 J kg   C) 1 15 J kg   D) 1 15 J kg   14. A body starts from rest from a point distant 0 r from the centre of the earth. It reaches the surface of the earth whose radius is R . The velocity acquired by the body is A) 0 1 1 2GM R r  B) 0 1 1 2GM R r        C) 0 1 1 GM R r  D) 0 1 1 GM R R        15. A smooth tunnel is dug along the radius of the earth that ends at the centre. A ball is released from the surface of earth along the tunnel if the coefficient of restitution is 0.2 between the surface and ball then the dis- tance travelled by the ball before second collision at the centre. A) 6 5 R B) 7 5 R C) 9 5 R D) 3 2 R 16. Two rings having masses M and 2M , re- spectively, having same radius are placed coaxially as shown in figure. 3R    R P If the mass distribution on both the rings is non-uniform, then gravitational potential at point P is A) 1 2 2 5 GM R         B) 2 1 2 GM R         C) zero D) cannot be determined from given information 17. A point P lies on the axis of a fixed ring of mass M and radius R , at a distance 2R from its centre O. A small particle starts from P and reaches O under gravitational attraction only. Its speed at O will be: A) 2 1 1 5 GM R        B) 2GM R C)   2 5 1 GM R  D) zero 18. Two cylindrical vessels of equal cross-sec- tional area contain water upto heights 1 h and 2 h . The vessels are inter connected so that the levels in them become equal. Calcualte the work done by the force of gravity during this process if  is the density of water: A) 2 1 2 2 h h  A g        B) 2 1 2 2 h h  A g        C) 2 2 1 Ah g h  D) 2 1 2 Ah g h  19. Gravitational potential at the centre of curva ture of a hemispherical bowl of radius R and mass M is V: A) Gravitational potential at the centre of c u r - vature of a thin uniform wire of mass M, be nt into a semicircle of radius R, is also equal to V B) In part (a) if the same wire is bent into a quar- ter circle then also the gravitational potential at the centre of curvature will be V C) In part (a) if the wire mass is non uniformly distributed along its length and it is bent intosemicircle of radius R, gravitational potential at the centre is 2V D) None of these 20. The gravitational field due to a mass