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A racing car travels on a track (without banking) ABCDEFA. ABC is a circular arc of radius 2R. CD and FA are straight paths of length R and DEF is a circular arc of radius R = 100 m. The co-efficient of friction on the road is μ = 0.1. The maximum speed of the car is 50 ms^(−1) . Find the minimum time for completing one round. |
Figure shows (x, t), (y, t) diagram of a particle moving in 2-dimensions. If the particle has a mass of 500 g, find the force (direction and magnitude) acting on the particle. |
Two blocks of masses M and 2M are connected to each other through a light spring as shown in figure. If we push the mass M with a force F which cause acceleration a in mass M, what will the acceleration in 2M? |
Two blocks A and B each of mass 1 kg are placed on a smooth horizontal surface. Two horizontal forces 5 N and 10 N are applied on the blocks A and B respectively as shown in figure. The block A does not slide on block B. Then the normal reaction between the two block is |
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A spring of force constant k is cut into two pieces such that one piece is twice as long as the other. Then the longer piece will have a force constant of |
Consider a block sliding over a smooth inclined surface of inclination θ. Relating to Newton′s second law applied on the block, select the incorrect alternative. (1) ΣF_(y′) ≠ 0 (2) ΣF_y = 0 (3) ΣF_x = −mg sin θ (4) ΣF_(x′) < 0 |
A bird sits on a stretched telegraph wire. The additional tension produced in the wire is (1) Zero (2) Greater than weight of the bird (3) Less than the weight of the bird (4) Equal to the weight of the bird |
A light rope is passed over a pulley such that at its one end a block is attached, and on the other end a boy is climbing up with acceleration (g/2) relative to rope. Mass of the block is 30 kg and that of the boy is 40 kg. Find the tension and acceleration of the rope. |
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There are two crystalline forms of PbO ; one is yellow and the other is red. The standard enthalpies of formation of these two forms are −217.3 and −219 kJ per mole respectively. Calculate the enthalpy change for the solid-solid phase transition. PbO (yellow) → PbO (red) |
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Motion in two dimensions, in a plane can be studied by expressing position, velocity and acceleration as vectors in Cartesian co-ordinates A^→ = A_x i^∧ + A_y j^∧ where i^∧ and j^∧ are unit vector along x and y directions, respectively and A_x and A_y are corresponding components of A^→ (Figure). Motion can also be studied by expressing vectors in circular polar co-ordinates as A^→ = A_r r^∧ + A_θ θ^∧ where r^∧ = (r^→ /r) = cos θ i^∧ + sin θ j^∧ and θ^∧ = −sin θ i^∧ + cos θ j^∧ are unit vectors along direction in which ′r′ and ′θ′ are increasing. (a) Express i^∧ and j^∧ in terms of r^∧ and θ^∧ (b) Show that both r^∧ and θ^∧ are unit vectors and are perpendicular to each other. (c) Show that (d/dt)(r^∧ ) = ωθ^∧ where ω = (dθ/dt) and (d/dt)(θ^∧ ) = −ωr^∧ (d) For a particle moving along a spiral given by r^→ = αθr^∧ , where α = 1 (unit), find dimensions of ′α′. (e) Find velocity and acceleration in polar vector representation for particle moving along spiral described in (d) above. |
An elastic material has a length of 36cm when a load of 40N is hung on it and a length of 45cm when a load of 60N is hung on it. what is the Original length of the string ? |
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Argon diffuses through a hole under prescribed condition of temperature and pressure at the rate of 3cm^3 per velocity. At what velocity will helium diffuse through the same hole under the same condition (Ar = 29.94 g, He = 4g). |
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A block of mass M is pulled vertically upward through a rope of mass m by applying force F on-one end of the rope. What force does the rope exert on the block? |
The work function of a metal is 4 eV. If light of frequency 2.3 × 10^(15) Hz is incident on metal surface, then, (1) No photoelectron will be ejected (2) 2 photoelectron of zero kinetic energy are ejected (3) 1 photoelectron of zero kinetic energy is ejected (4) 1 photoelectron is ejected, which required the stopping potential of 5.52 volt |
The energy required to dislodge electron from excited isolated H-atom, IE_1 = 13.6 eV is (1) = 13.6 eV (2) > 13.6 eV (3) < 13.6 eV and > 3.4 eV (4) ≤ 3.4 eV |
In moving a body of mass m up and down a rough incline plane of inclination θ, work done is (S is length of the planck, and μ is coefficient of friction). |
The acceleration of an object is given by a(t) = cos(nπ), and its velocity at time t = 0 is (1/(2π)). Find both the net and the total distance traveled in the first 1.5 seconds. |
A particle of mass 1 gram executes an oscillatory motion on the concave surface of a spherical dish of radius 2 m, placed on a horizontal plane. If the motion of the particle starts from a point on the dish at the height of 1 cm from the horizontal plane and the coefficient of friction is 0.01, how much total distance will be moved by the particle before it comes to rest? |
In an atom the last electron is present in f-orbital and for its outermost shell the graph of Ψ^2 has 6 maximas. What is the sum of group and period of that element? |
Pg 131 Pg 132 Pg 133 Pg 134 Pg 135 Pg 136 Pg 137 Pg 138 Pg 139 Pg 140 |