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Example of gravitation Gravitation Example . A solid sphere of lead has a mass M and radius R. A spherical cavity is made in it (fig.1) , the boundary passing through the centre O and also touching the boundary of the solid sphere, Find the gravitational force on a mass m placed at point P, distance r from O, along the line of ceneres. Solution : Let M be the mass and ρ be the density of the entire solid sphere. Let C be the centre of the spherical cavity. For an external point, the massive sphere behaves as if its entire mass is concentrated at its centre O. The gravitational attraction on a body of mass M at P due to complete solid sphere with centre at O is: F 1 =GMm/r 2 ; along PO The diameter of smaller sphere at place of hollow spherical cavity is R . Its radius is R/2. Therefore mass of this sphere is : M’ =(4/3)π(R/2) 3 ρ=(1/8){(4/3)πR 3 ρ}=M/8 The gravitational force on m due to this small sphere with centre at C is F 2 = GM’m/(r-R/2) 2 = {G(m/8)m}/(r-R/2) 2  ...

10 Question-Answer on rotational mechanics 1.        A fly wheel rotating about a fixed axis has a kinetic energy of 360 joul when its angular speed is 30 radian/sec. The moment of inertia of the wheel about the axis of rotation is: (a)     0.6 kg m 2 (b)    0.15 kg m 2 (c)     0.8 kg m 2 (d)    0.75 kg m 2 Ans: (c) 2.        A rigid spherical body is spinning around an axis without any external torque. Due to change in temperature, the volume increases by 1%. Its angular speed will be: (a)       Increases approximately by 1% (b)    decreases approximately by 1% (c)     decreases approximately by0.67% (d)    decreases approximately by 0.33% Ans: (c ) 3.        A thin uniform circular ring is rolling down an inclined plane of inclination 30˚ without slipping. Its linear ac...

10 Question-Answer on moment of inertia 1.        Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an axis └ to its plane and passing through a point on its rim will be: (a)     5 I (b)    3 I (c)     6 I (d)    4 I Ans :( c) 2.        The moment of inertia of a body about a given axis is 1.2 kg m 2 Initially, the body is at rest .In order to produce a rotational kinetic energy of 1500 joule, an angular acceleration of 25 radian/s 2 must be applied about that axis far a duration of : (a)     4 sec (b)    2 sec (c)     8 sec (d)    10 sec Ans: ( b) 3.        A hoop o mass M and radius R is suspended on a peg in a wall. Its moment of inertia about the peg is : (a)     2MR 2 (b)    MR 2 (c)  ...

 10 Question- Answer on centre of mass 1.        The unit of position vector of centre of mass is (a)     Metre (b)    Kg (c)     Kg-m 2 (d)    Kg-m Ans(a) 2.        Two particles of masses m 1 and m 2 (m 1 > m 2 ) attract each other with a force inversely proportional to the square of the distance between them. If the particles are initially held at rest and then released, the centre og mass will (a)     Move towards m 1 (b)    Move towards m 2 (c)     Remain at rest (d)    Nothing can be said Ans: (c) 3.        A system consists of three particles, each of mass m and located at (1, 1), (2, 2) and (3, 3) .The co-ordinates of the centre of mass are? (a)     (1, 1) (b)    (2, 2) (c)     3, 3) (d)    (6, 6) An...

10 Question – Answer on circular motion 1.        A car takes a turn around a circular curve. If it turns at double the speed, the tendency to overturn is: (a)     Halved (b)    Doubled (c)     Quadrupled (d)    Unchanged Ans: (c) 2.        A particle of mass 2 kg is moving along a circular path of radius 1 m. If its angular speed is 2π rad/ s, the centripetal force will be (a)     4 πN (b)    4 π 2 N (c)     8 πN (d)    8 π 2 N Ans: ( d) 3.        For a particle moving along a circular path with a constant speed, the acc. Is constant in: (a)     Magnitude (b)    Direction (c)     Both magnitude and direction (d)    neither magnitude nor direction Ans : ( a) 4.        A stone is tied ...

Example of rotational motion Example of rotational motion - A circular plate of uniform thickness has a diameter of 56 cm. A circular portion of diameter 42 cm is removed from one edge of the plate as shown in fig.1. Find the position of centre of mass of the remaining portion? Solution :   Area of whole plate = π (56/2) 2 = 784 π   sq. cm. Area of cutout portion = π (42/2) 2 = 441 π   sq. cm. Area of remaining portion, Fig 1 = 784 π – 441 π= 343 π cm 2 As mass is proportional to area Mass of cutout portion/mass of remaining portion =   m 1 /m 2 = 441 π/343 π= 9/7 Let C 2 be centre of mass of remaining portion and C 1 be centre of mass of cutout portion. O is centre of mass of the whole disc. OC 1 = r 1 = 28-21= 7 cm. OC 2   = r 2 = ? Equating moments of masses about O, we get m 2 × r 2 = m 1 × r 1 r 2 = 9

10 Question-Answer on work power energy 1.        If two protons are brought near one another, the potential energy of the system will: (a)     Increase (b)    Decrease (c)     Remain the same (d)    Equal to the kinetic energy Ans:   (a) 2.        A water pump driven by petrol raises water at a rate of 0.5 m 3 /min. from a depth of 30 m. If the pump is 70% efficient the power developed by the engine is: (a)     1750 W (b)    2450 W (c)     3500 W (d)    7000 W Ans: ( c)   3.        The energy required to accelerate a car from 10 m/s to 20 m/s is n times the energy required to accelerate the same from rest to 10 m/s, where n is : (a)     1 (b)    4 (c)     2 (d)    3 Ans: ( d)   4.   ...