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Radius Rod
Test Series – 3(a)
26. The trajectory of a projectile in a vertical plane is y = ax – bx2, where a and b are constants and x and y are respectively horizontal and vertical distances of the projectile from the point of projection. The maximum height attained by the particle and the angle of projection from the horizontal are :
(A) (B) (C) (D)
27. Force acting on a particle is N. Work done by this force is zero, when a particle is moved on the line 3y + kx = 5. Hence the value of k is :
(A) 2 (B) 4 (C) 6 (D) 8
28. A conductor with rectangular cross section has dimensions (a ´ 2a ´ 4a) as shown in figure. Resistance across AB is x, across CD is y and across EF is z. Then :
(A) x = y = z (B) x > y > z
(C) y > z > x (D) x > z > y
29. Refraction takes place at a concave spherical boundary separating glass air medium. For the image to be real, the object distance (mg = 3/2)
(A) should be greater than three times the radius of curvature of the refracting surface
(B) should be greater than two times the radius of curvature of the refracting surface
(C) should be greater than the radius of curvature of the refracting surface
(D) is independent of the radius of curvature of the refracting surface
30. A right-angled prism is made up of a material of refractive index m. It is desired that a light ray incident normally on PQ emerges parallel to the incident direction after suffering two total internal reflections. In which of the following conditions is this possible ?
(A) (B) (C) m = 1.3 (D) Never possible
31. A 100 W bulb and a 25 W bulb are designed for the same voltage. They have filaments of the same length and material. The ratio of the diameter of the 100 W bulb to that of the 25 W bulb is :
(A) 4 : 1 (B) 2 : 1 (C) (D) 1 : 2
32. A particle of mass m attached to a string of length l is describing circular motion on a smooth plane inclined at an angle a with the horizontal. For the particle to reach the highest point its velocity at the lowest point should exceed.
(A) (B) (C) (D)
33. A particle is moving in a circle of radius R in such a way that at any instant the total acceleration makes an angle of with radius. Initial speed of particle is v0. The time taken to complete the first revolution is :
(A) (B) (C) (D)
34. Three blocks A, B and C of equal mass m are placed one over the other on a smooth horizontal table as shown in figure. Coefficient of friction between any two blocks of A, B and C is 1/2. The maximum value of mass of block D so that the blocks A, B and C move with slipping over each other is :
(A) 6m (B) 5m (C) 3m (D) 4m
35. A bead of mass m is attached to one end of a spring of natural length R and spring constant . The other end of the spring is fixed at point A on a smooth vertical ring of radius R as shown in figure. The normal reaction at B just after it is released to move is :
(A) (B) (C) (D)
36. A particle is displaced from to x = + 6m. A force F acting on the particle during its motion as shown in figure. Graph between work done by this force (W) and displacement (x) should be :
(A) (B)
(C) (D)
37. The potential energy of a particle of mass m is given by for x < 0 and U = 0 for . If total mechanical energy of the particle is E, then its speed at is :
(A) zero (B) (C) (D)
38. Eight resistors and a battery of negligible internal resistance are connected as shown in the figure, the current through 10 ohm resistor is 3A and that through 7 ohm resistor is zero.
I. The value of r is 15
II. The current through is 2A
III. The emf of the battery is 45V
IV. The current through is 3.33 A
Which is the correct option?
(A) I, II, III, IV (B) II, III
(C) II, III, IV (D) I, III, IV
39. In the circuit shown in figure potential difference between points A and B is 16V. The current through resistance will be :
(A) 2.5 A (B) 3.5 A (C) 4.0 A (D) zero
40. In the arrangement shown in figure m1 = 1 kg, m2 = 2 kg. Pulleys are massless and strings are light. For what value of M the mass m1 moves with constant velocity (neglect friction) :
(A) 6 kg (B) 4 kg (C) 8 kg (D) 10 kg
41. A block of mass m is pressed against a wall by a spring as shown in the figure. The spring has natural length , and the coefficient of friction between the block and the wall is . The minimum spring constant K necessary for equilibrium is :
(A) (B) (C) (D)
42. A block A of mass M rests on a wedge on a wedge B of mass 2M of inclination . There is sufficient friction between A and B so that A does not slip on B. If there is no friction between B and ground, the compression in the spring is :
(A) (B)
(C) (D) zero
43. Two particles are projected from a point at the same instant with velocities whose horizontal and vertical components are u1, v1 and u2 and v2 respectively. The interval between their passing through the other common point of their path is :
(A) (B) (C) (D) None
44. The floor shown in figure is smooth and friction exists only between m1 and m2. Here we have m1 = 20 kg, m2 = 30 kg. If F = 180 N, the acceleration of m1 and m2 is :
(A) a = 3.6 m/s2(B) a = 4.6 m/s2
(C) a = 2.67 m/s2 (D) a = 7.2 m/s2
45. A cylindrical glass tube is folded in a circle as shown in figure. The maximum value of d/R so that the beam of light incident normally at the face A emerges through face
(A) 0.5 (B) 0.41 (C) 2 (D) 1.41
46. A thin uniform rod of mass m moves translationally with acceleration a due to two anti-parallel forces on moment arm . One force is of magnitude F and acts at one extreme end. The length of the rod is :
(A) (B)
(C) (D)
47. A light triangular plate ABC of mass m is free to rotate in the vertical plane about a fixed horizontal axis through A. It is supported by a string such that the side AB is horizontal. The reaction at the support A is :
(A) (B)
(C) (D) mg
48. A wheel is rolling without sliding on a horizontal surface. The centre of the wheel moves with a constant speed v0. Consider a point P on the rim which is at the top at time t = 0. The square speed of point P is plotted against time t. The correct plot is (R is radius of the wheel).
(A) (B) (C) (D)
49. The K.E. of a particle moving along a circle of radius r is, where x is the distance covered. What is the force acting on the particle ?
(A) (B) (C) (D)
50. A bank of cells having a total emf of 12.0 volts and negligible internal resistance is connected in series with two resistors. A voltmeter of resistance is connected across the resistors in turns and measured 4 V and 6 V respectively. Then the value of the two resistances are (respectively) :
(A) (B)
(C) (D)
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Find the numbers of atoms in a copper rod with a length of 9.85 cm and a radius of 1.05 cm. the densityis 8.96
first and foremost, what is the unit of the density? is it g/mL kg/L or kg/m^3 etc... Or is it the specific gravity?
If 8.96 is the specific gravity multiply it wth 1g/mL to convert it to density = 8.96g/mL.
next compute the volume of the copper rod:
(3.1416)(radius)^2(length) = volume
to have the mass of the copper:
(density)(volume) = mass of copper
(8.96)(volume) = mass of copper
from the mass of copper convert to number of moles:
(mass of copper)/(atomic weight of copper) = number of moles of copper
from moles to number of atoms:
(number of moles of copper)(avogadro's number) = number of atoms of copper
(number of moles of copper)(6.022x10^23) = number of atoms of copper
Radius rod pin repair, rat rod