This section contains questions the answer to each of the question is a single digit integer, ranging from 0 to9. The appropriate bubbles have to be darkened. For example, if the correct answers to question
Numbers
1, 2, 3, 4, 5, 6, 7 and 8 (say ate 1,4, 3, 5, 8, 2, 9 and 6 respectively, then the correct darkening of bubbles will look like as shown.
12. The rod is placed on the edge of a tumbler with water so that half of ball is submerged in water when the system is in equilibrium. Density of ball =2700 kg/m3, radius of ball is 0.5 cm and mass of rod =4.4 gram. Find 2y/x
13. A fixed U-shaped smooth has semi-circular bending between A and as shown in the figure.
A bead of mass 1/2 kg moving with uniform speed√∏ through the wire enters the semicircular bend at A and leaves at B. Find the magnitude of average force exerted by the bead on the part AB of the wire.
14. .A gas is enclosed in a vessel at a constant temperature at a pressure of 2atm and volume 4 litres. Due to a leak in the vessel, after some time the pressure is reduced to 1.5 atm. As a result 5v% of the gas as escaped out. What is the value of v?
15. 2 kg ice at -20°C is mixed with 5 kg water at 20°C. Then what is the final amount of water in
the mixture? Given specific heat of ice =0.5 cal/g°C, specific heat of water = 1 cal/g°C, Latent heat of fusion of ice = 80 cal/g.
16.A particle of mass 5000g is moving horizontally with a constant velocity 1m/s towards a rigid wall that is moving in opposite direction with a constant speed 2m/s. Assuming elastic impact between the particle and wall find the work done by the wall in reflecting the particle.
17.A bead of mass 2m can slide on a smooth rod . A particle of mass m is attached to the bead by a light string of length l. Initially the particle is held horizontally in level with the bead and the string held just taut. If the distance through which the bead will move when the string has turned through an angle is x/30 with the horizontal,, then find the value of x (in SI units)?
[take θ=60°,l=lm ]
18. A particle moves in a circle of radius R with a constant speed v. then, find the magnitude of
average acceleration during a time interval∏R/2v .
Take v=√2∏ and R=√2.
19. An elastic ball of mass 1/2 kg is suspended from a fixed point by an inextensible string. A small particle of same mass moving ’downwards at an angle of 37° with the vertical hits the ball directly with the velocity 17m/s if the coefficient of restitution is 4/5 then determine the impulsive tension (i.e; impulse) in the string at the instant of collision.