Com of Solid Bodies
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Q. PL32. The time period of spring block system is T. Thespring is cut into two parts with their length in ratioof 2: 3. Find the time period of oscillation of sameblock with longer part of spring(2) 2т, ЗК(1) 2TKЗт2m(4) 2t5K(3) 2T5K
Q. 40. A rod of weight W is supported by two parallel knife edges A and B is in equilibrium in a horizontal position.The knives are at a distance d from each other.The centre of mass of the rod is at distance x from A.The normal reaction pn A is 1)W(d-x)/d 2)Wx/d 3)Wd/x 4)W(d-x)/x
Q. Four particles of equal masses are moving round a circle of radius r due to their mutual gravitation attraction. Find the angular velocity.
Q. A sphere of diameter r is cut from a sphere of radius r such that the centre of mass of the remaining mass be at maximum distance from original centre; then the distance is
Q. Three identical bodies of equal mass m each are moving along a circle of radius r under the action of their mutual gravitational attraction. the speed of each body is :-Three identical bodies of equal mass m each are moving along a circle of radius r under the action of their mutual gravitational attraction. the speed of each body is :
Q. An object of mass M is divided into two parts , which are placed at a distance of d .if the gravitational force of attraction is maximum between parts , then find the ratio of mass of both parts
Q. 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 ?
Q. A uniform solid hemisphere of radius r is joined to a uniform solid right circular cone of base radius r. Both have same density. The centre of mass of the composite solid lies on the common face. The height (h) of the cone is
Q. Two discs having masses in the ratio 1:2 and radii in the ratio 1:8 roll down without slipping one by one from an inclined plane of height h. The ratio of their linear velocities on reaching the ground i
Q. four point masses are placed at the center of a square oc side 2 m as shown in figure . Find the center of mass of the system w.r.t. the center oc squar
Q. A particle executed SHM according to equations 4d^2x/dt^2 +320x =0 it time period of oscillations
Q. 33. A straight rod of length L has one of its ends at origin and the other at x=L. If the mass per unit length of the rod is given by Ax where A is constant, where is its mass centre?
Q. 63. A disc of mass m and radius r is free to rotate about its centre as shown in the figure. A string is wrapped over its rim and a block of mass m is attached to the end of the string. The system is released from rest. The speed of the block as it descends through a height h, is
Q. A uniform rod of mass m and length l is suspended about its end time period of small angular oscillations is
Q. 8) Toal energy of a particle of mass 100 g moving along x-axis is given by U 5x(x-4 in metre. The period of oscillation is
Q. consider a system of 2 particles having mass m1 and m2 .if the particle m1 is pushed towards m2 through a dis†an ce d , by what dis†an ce should be particle mass m2 be moced so as to keep the centre of mass of the system of particles at the original pition
Q. One end of a cylindrical pipe has radius of 2cm.water comes out at 10m/s. Rate at which mass is leaving the pipe is
Q. 22. Two men each of mass m stand on the rim of a horizontal circular disc, diametrically opp. To each other. The disc has mass M and is free to rotate about a vertical axis passing through its centre of mass. Each mass start simultaneously along the rim clockwise and reaches their original starting points on the disc. The angle turned by the disc wrt the ground in radian is??
Q. 60.A man has constructed a toy. If the density of the material of the sphere is 12 times that of the cone then determine the position of the centre of mass.[Centre of mass of a cone of height h is at height of h/4 from its base]
Q. 7. A particle is free to move on x-axis, in which of thefollowing case, the particle will execute oscillationabout x 1?(1) F = (x - 1)(2) F =- (x - 1)2(3) F =- (x- 1)3(4) F = (x- 1)3
Q. FORMULA FOR APPARENT WEIGHT IS
Q. Two particles of mass m and 2m are initially at restat a separation of 2d. Find their velocity ofapproach due to gravitational attraction, whenseparation is d.
Q. A uniform solid hemisphere of radius r is joined to a uniform solid right circular coneof base r and height \sqrt{3r.if both have same density then find position of centre of mass from the centre of hemisphere
Q. A parabolic bowl with its buttom at origin has the shape y=x^2/20. The maximum height to which a small mass m can be placed on the bowl without slipping is(μ=0.5)?
Q. a solid cylinder of mass 2kg and radius 50cm rolls up an inclined plane of angle of inclination 30 degree the centre of mass of cylinder has speed of 4m\s the distance travelled by the cylinder surface will be
Q.
A man of mass m is standing on a stationary wooden board of mass M kept on smooth ice. The man starts running on the board and acquires a speed u relative to the board. Find the speed of the man relative to stationary observer. The board is long enough.
Q. 5. A ball of mass 100 g is suspended by a string 40 cmlong. Keeping the string taut, the ball describes ahorizontal circle of radius 10 cm. Find the angular
Q. In a model of universe two particle each of mass M are revolving in a circle of radius R under mutual gravitational attraction their linear velocities are
Q. a) 02. A system consists of two masses conby a massless rod lies along x-axis. The diof centre of mass from O isa) ob) 2m c) 5md) 7mZin
Q. 14. Locate center of mass in a sector with angle 60 degree and M mass and R radius?
