This section contains 8 multiple choice questions. Each question has 4 choices {a), (b), (c) and (d), out of which ONLY ONE is correct.
1. A U-tube containing a liquid is accelerated horizontally with a constant acceleration equal to g/5 where g is the acceleration due to gravity. The separation between the vertical limbs l, while the initial level of the liquid in each arm is also 1, The difference in the heights of liquid in two vertical limbs is, in the steady state,
2. A thin uniform spherical shell and a uniform solid cylinder of the same mass and radius are allowed to roll down a fixed incline, without slipping, starting from rest. The times taken by them to roll down the same distance are in the ratio,
3.A planet of radius R has an acceleration due to gravity of g on its surface. A deep smooth tunnel is dug on this planet, radially inward, to reach a point P 1ocatec at a distance of R/2 from the centre of the planet. Assume that the planet has uniform density. The kinetic energy required to be given to a small body of mass m, projected radially
outward from P, so that it gains a maximum altitude equal to the thrice the radius of the planet from its surface, is equal to
4. A horizontal uniform beam AB of length 4 m and a mass of 20 kg is supported at the end B by means of a string which passes over a fixed, smooth pulley supporting a counterbalancing weight of 8 kg on the other side. What force, F, when applied at the point A in suitable direction, will hold the beam in static equilibrium?
(d) no. force F, as specified, can hold the beam in static equilibrium
5. Two identical spheres A and B each of mass M and radius R are moving on a horizontal surface as shown. The angular momentum of the sphere A about the topmost point of the sphere B is
6. A vessel contains oil’(density0.8 g/cc) over mercury ‘(density 13.6 g/cc). A homogeneous sphere floats with half its volume immersed in mercury and other half in oil. The density of the material of
Sphere in g/cc is
(a)3.3 (b)6.4 (c)7.2 (d)22.8
7. Block A of mass M in the figure is released from the rest when the extension in the spring is x0. The maximum downward displacement of the block is
8. Velocity-time graph of a particle moving in a straight line is shown in the figure. Mass of the particle is 2kg. Work done by all the forces acting on the particle in time interval t =0 to t = 10 sec is