An archery target has three regions formed by three concentric circles as shown in Figure. If the diameters of the concentric circles are in the ratio 1: 2:3, then find the ratio of the areas of three regions.
Two uniform solid spheres
of equal radii R, but mass M and 4 M have
a centre to centre separation 6 R, as shown
in Fig. 7.10. The two spheres are held fixed.
A projectile of mass m is projected from the
surface of the sphere of mass M directly
towards the centre of the second sphere.
Obtain an expression for the minimum
speed v of the projectile so that it reaches
the surface of the second sphere.
All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if area of the circle is 1256 cm2. .(Use π = 3.14).
Find the potential energy of
a system of four particles placed at the
vertices of a square of side l. Also obtain
the potential at the centre of the square.
Three equal masses of m kg
each are fixed at the vertices of an
equilateral triangle ABC.
(a) What is the force acting on a mass 2m
placed at the centroid G of the triangle?
(b) What is the force if the mass at the
vertex A is doubled ?
Take AG = BG = CG = 1 m (see Fig. 7.5)
Let the speed of the planet
at the perihelion P in Fig. 7.1(a) be vP and
the Sun-planet distance SP be rP. Relate
{rP, vP} to the corresponding quantities at
the aphelion {rA, vA}. Will the planet take
equal times to traverse BAC and CPB ?
Floor of a room is of dimensions 5 m × 4 m and it is covered with circular tiles of diameters 50 cm each as shown in Figure. Find the area of floor that remains uncovered with tiles. (Use π = 3.14)
Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 1.0 m apart ona horizontal table. What is the gravitational force and potential at the mid point ofthe line joining the centres of the spheres ? Is an object placed at that point inequilibrium? If so, is the equilibrium stable or unstable ?
On a square cardboard sheet of area 784 cm2, four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square sheet not covered by the circular plates.
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