DPP – 29
1. A uniform rod of length L is hanging from a ceiling. The variation of tensile stress with distance X from the ceiling is best represented by
(a) (b)
(c) (d)
2. A uniform steel wire hangs from the ceiling and elongates due to its own weight. The ratio of elongation of the upper half of the wire to the elongation of the lower half of wire is
(a) 4 : 1 (b) 3 : 1 (c) 3 : 2 (d) None
3. Select the correct statement on the basis of the given graph
(a) Young's modulus of A is greater but it is less ductile
(b) Young's modulus of A is greater and it is more ductile
(c) Young's modulus of A is less and it is less ductile (d) Young's modulus of A is less but it is more ductile
4. A steel rope of length L, area of cross-section A, Young’s modulus Y, is hanging from a celling in equilibrium. The elastic potential energy per unit volume at a point L/3 from ceiling is [Density = d]
(a) 2(dgL)2/9Y (b) (dgL)2/9Y
(c) 2(dgL)/9AY (d) 2(dgL)2/3Y
5. Disk A of radius r moving on perfectly smooth surface at a speed v collides elastically with an identical stationary disk B. If the impact parameter is r/2 as shown, the velocity of the disk B after collision will be (a) 4 15 v (b) 4 v (c) 2 v (d) v 2 3
ring at which the ring breaks. The wire breaks at tensile stress . Ignore gravity. (Take
= 4 and r = 1m)
7. A wire having cross-sectional area S is attached to wall on one side and a block of mass M on the other side which placed on a horizontal surface having coefficient of friction as shown. Material of wire has coefficient of thermal expansion and Young's modulus Y. At initial temperature there is no stress in the wire. Now the wire is cooled. Determine the decrease in temperature (in °C) when the block will begin to move (Take Mg = 4Y and S = 2 m2
)
8. A ball is thrown from origin with a velocity u(5iˆ15ˆj10kˆ)m/s. The ball hits an inclined plane at point P as shown. Find the time taken (in s) by the ball to reach point P.
O P u x z y 45° r
DPP – 30
1. A bucket contains water filled up to a height of 15 cm. The bucket is tied to a rope which is passing over a frictionless light pulley and the other end of the rope is tied to a block whose mass is half of that of the combined mass of bucket and water. If the system is released from rest, the gauge pressure at the bottom of the bucket will be
(a) 0.5 kPa (b) 1 kPa
(c) 5 kPa (d) None of these
2. A fire hydrant delivers water of density at a volume rate of L. The water travels vertically upward through the hydrant and then turns 90° turn to emerge horizontally at speed V. The pipe and nozzle have uniform cross-section throughout. The force exerted by the water on the corner of the hydrant is
(a)VL (b) zero (c) 2VL (d) 2 VL
3. A Newtonian fluid fills the clearance between a shaft and a sleeve. When a force of 800N is applied to the shaft, parallel to the sleeve, the shaft attains a speed of 1.5 cm/sec. If a force of 2.4 kN is applied instead, the shaft would move with a speed of
(a) 1.5 cm/sec (b) 13.5 cm/sec (c) 4.5 cm/sec (d) None
4. If the system is not in free fall, the correct statement about hydrostatic pressure is (a) in a liquid, points at different depths can never be at same pressure.
(b) in a liquid, points at different depths may be at same pressure.
(c) in different liquids, points at same depth can never be at different pressure. (d) in different liquids, points at same depth can be at same pressure.
5. A particle moving with kinetic energy of 3 joule makes an elastic head on collision with a stationary particle having twice its mass. The incorrect statement is
(a) The minimum kinetic energy of the system is 1 joule. (b) The maximum elastic potential energy of the system is 2 joule.
(c) Momentum and total kinetic energy of the system are conserved at every instant.
(d) The ratio of kinetic energy to potential energy of the system first decreases and then increases.
6. A block of wood weighs 12 kg and has a relative density 0.6. It is to be in water with 0.9 of its volume immersed. A metal of relative density 14 is attached below the block. Find the weight (in N) of metal needed.
7. A spherical tank of 1.2 m radius is half filled with oil of relative density 0.8 . If the tank is given a horizontal acceleration of 10 m/s2. The maximum pressure on the tank
section A floats in a liquid of density d2 contained in a vessel (d2> d1). The bottom of the cylinder just rests on a spring of constant k. The other end of the spring is fixed to the bottom of the vessel. Determine the weight (in N) that may be placed on top of the cylinder such that the cylinder is just submerged in the liquid. (Take l = 1m, d1 1200kg/m3,
d2= 2000 kg/m3, K = 1000 N/m, A = 0.1 m2and g = 10 m/s2)
9. A plank OA rotates in vertical plane about a horizontal axis through O with a constant counter clockwise angular velocity of 3 rad/sec. As it passes the position = 0, a small mass m is placed upon it at a radial distance (r) of 0.5 m. If the mass is observed to slip at = 37º, the coefficient of friction between the mass and the plank is
1000 n
. Find the value of n.
DPP – 31
1. The tank in fig discharges water at constant rate for all water levels above the air inlet R. the heights above datum to which water would rise in the manometer tubes M and N is respectively
(a) 30cm, 60cm (b) 40cm, 60cm
(c) 20cm, 40cm (d) 20cm, 60cm
2. In the figure shown a particle P strikes the inclined smooth plane horizontally and rebounds vertically. If the angle is 60°, then the coefficient of restitution is:
(a) 1/3 (b) 1/ 3 (c) 1/2 (d) 1
3. A uniform aluminium ball of radius r is suspended through a light string from the end of an uniform horizontal rod of mass M placed horizontally on the edge of a container filled with water. The system is under equilibrium and ball is half submerged in water. Neglect surface tension of water. The ratio
x y will be (Given 100 3 4 3 M r , density of ball = 2.7 × 103 kg/m3, density of water = 1 × 103kg/m3). x y (a) 40 (b) 45 (c) 30 (d) 35
4. A cubical box of liquid has a small spout located in one of the bottom corners. When the box is full and placed on a level surface, opening the spout results in the flow of liquid with an initial speed of v0as shown in figure. When the box is half empty, it is tilted at 45° so that the spout is at the lowest point. Now, the opening of spout will allow the liquid to flow out with a speed of v0 (a) v0 (b) 2 0 v (c) 2 0 v (d) 4 0 2 v
5. A jug contains 15 glasses of orange juice. When you open the tap at the bottom it takes 12 sec to fill a glass with juice. If you leave the tap open. How long will it take (in s) to fill the remaining 14 glasses and thus empty the jug? ( 153.9, 143.7)
6. A large tank is filled with two liquids of specific gravities 2 and . Two holes are made on the wall of the tank as shown. The ratio of the distances from O of the points on the ground where the jets from holes A & B strike is
b
the point A in a U tube at rest. The height of liquid column above A is 8a/3 where AB = a. The cross sectional area of the tube is S. With what angular velocity (in rad/s) the tube must be whirled about a vertical axis at a distance a such that the interface of the liquids shifts towards B by 2a/3. (Take a =
19 180
unit and g = 10 m/s2)
8. A child of mass 4 kg jumps from cart B to cart A and then immediately back to the cart B. The mass of each cart is 20kg and they are initially at rest. In both cases the child jumps at 6m/s relative to the cart. If the cart moves along the same line with negligible friction with the final velocities of v andB vArespectively. Find the
ratio of 6vB and 5vA.
