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General
Easy
Question
In the figure shown a semicircular area is removed from a uniform square plate of side ‘ l ’ and mass ‘m’ (before removing). The x-coordinate of centre of mass of remaining portion is (The origin is at the centre of square)
The correct answer is:
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Physics-
Consider the system shown in figure. Pulley, string and spring are ideal and Dm << M. Initially spring is in it’s natural length and both the blocks are at rest. (Assume that initially Dm was situated at origin). Maximum y coordinate of Dm in subsequent motion is xmg/k then value of x is
Consider the system shown in figure. Pulley, string and spring are ideal and Dm << M. Initially spring is in it’s natural length and both the blocks are at rest. (Assume that initially Dm was situated at origin). Maximum y coordinate of Dm in subsequent motion is xmg/k then value of x is
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A steel wire is rigidly fixed along diameter of aluminium ring of radius R as shown. Linear expansion coefficient of steel is half of linear expansion coefficient for aluminium, then the thermal stress developed in steel wire is: (aAl is linear expansion coefficient for aluminium and Young’s modulus for steel is Y
A steel wire is rigidly fixed along diameter of aluminium ring of radius R as shown. Linear expansion coefficient of steel is half of linear expansion coefficient for aluminium, then the thermal stress developed in steel wire is: (aAl is linear expansion coefficient for aluminium and Young’s modulus for steel is Y
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Figure shows isosceles triangle frame ABC of two different material shown in figure. Thermal expansion cofficient of the rod ADB is a1 and for rod ACB is a2 . End C is fixed and whole system is placed on smooth horizontal surface and D is midpoint of rod AB and CD is perpendicular to the AB. If temperature of the system is increase such as it is found that distance CD remain fixed the
Figure shows isosceles triangle frame ABC of two different material shown in figure. Thermal expansion cofficient of the rod ADB is a1 and for rod ACB is a2 . End C is fixed and whole system is placed on smooth horizontal surface and D is midpoint of rod AB and CD is perpendicular to the AB. If temperature of the system is increase such as it is found that distance CD remain fixed the
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A wire is bent in a parabolic shape followed by equation x = 4y2 . Consider origin as vertex of parabola. A wire parallel to y axis moves with constant speed 4 m/s along x-axis in the plane of bent wire. Then the acceleration of touching point of straight wire and parabolic wire is (when straight wire has x coordinate = 4 m) :
A wire is bent in a parabolic shape followed by equation x = 4y2 . Consider origin as vertex of parabola. A wire parallel to y axis moves with constant speed 4 m/s along x-axis in the plane of bent wire. Then the acceleration of touching point of straight wire and parabolic wire is (when straight wire has x coordinate = 4 m) :
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All the rods have same conductance ‘K’ and same area of cross section ‘A’. If ends A and C are maintained at temperature 2T0 and T0 respectively then which of the following is/are correct:
All the rods have same conductance ‘K’ and same area of cross section ‘A’. If ends A and C are maintained at temperature 2T0 and T0 respectively then which of the following is/are correct:
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Two large non conducting plates having surface charge densities + s and –s respectively, are fixed d distance apart. A small test charge q of mass m is attached to two non conducting springs each of spring constant k as shown in the figure. The sum of lengths of both springs in undeformed state is d. The charge q is released from rest with both the springs nondeformed. Then charge q will (neglect gravity)
Two large non conducting plates having surface charge densities + s and –s respectively, are fixed d distance apart. A small test charge q of mass m is attached to two non conducting springs each of spring constant k as shown in the figure. The sum of lengths of both springs in undeformed state is d. The charge q is released from rest with both the springs nondeformed. Then charge q will (neglect gravity)
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As shown in the figure a variable force F is applied on conducting wire of length l such that its velocity remains constant. There is no resistance in any branch in the circuit. Consider the motion of wire from t = 0 initially there is no current in inductor. Now when wire has covered a distance x (from initial position) then at that time energy of inductor will be: (Neglect gravity)
As shown in the figure a variable force F is applied on conducting wire of length l such that its velocity remains constant. There is no resistance in any branch in the circuit. Consider the motion of wire from t = 0 initially there is no current in inductor. Now when wire has covered a distance x (from initial position) then at that time energy of inductor will be: (Neglect gravity)
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The state of an ideal gas is changed through an isothermal process at temperature T0 as shown in figure. The work done by gas in going from state B to C is double the work done by gas in going from state A to B. If the pressure in the state B is 
then the pressure of the gas in state C is :
The state of an ideal gas is changed through an isothermal process at temperature T0 as shown in figure. The work done by gas in going from state B to C is double the work done by gas in going from state A to B. If the pressure in the state B is then the pressure of the gas in state C is :
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P-T diagram is shown below then choose the corresponding V-T diagram
P-T diagram is shown below then choose the corresponding V-T diagram
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Physics-
A fixed container is fitted with a piston which is attached to a spring of spring constant k. The other end of the spring is attached to a rigid wall. Initially the spring is in its natural length and the length of container between the piston and its side wall is L. Now an ideal diatomic gas is slowly filled in the container so that the piston moves quasistatically. It pushed the piston by x so that the spring now is compressed by x. The total rotational kinetic energy of the gas molecules in terms of the displacement x of the piston is (there is vacuum outside the container)
A fixed container is fitted with a piston which is attached to a spring of spring constant k. The other end of the spring is attached to a rigid wall. Initially the spring is in its natural length and the length of container between the piston and its side wall is L. Now an ideal diatomic gas is slowly filled in the container so that the piston moves quasistatically. It pushed the piston by x so that the spring now is compressed by x. The total rotational kinetic energy of the gas molecules in terms of the displacement x of the piston is (there is vacuum outside the container)
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The side of the cube is 'l' and point charges are kept at each corner as shown in diagram. Interaction electrostatic potential energy of all the charges is :
The side of the cube is 'l' and point charges are kept at each corner as shown in diagram. Interaction electrostatic potential energy of all the charges is :
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For a given thermodynamic cyclic process, P – V indicator diagram is as shown in the figure. Process AB, BC & CA are isobaric, adiabatic & isothermal respectively. Then which of the following curve represent correct V – T indicator diagram for the process ABCA?
For a given thermodynamic cyclic process, P – V indicator diagram is as shown in the figure. Process AB, BC & CA are isobaric, adiabatic & isothermal respectively. Then which of the following curve represent correct V – T indicator diagram for the process ABCA?
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One mole of an ideal gas is kept enclosed under a light piston (area=10– 2 m2 ) connected by a compressed spring (spring constant 100 N/m). The volume of gas is 0.83 m3 and its temperature is 100K. The gas is heated slowly so that it compresses the spring further by 0.1 m. The work done by the gas in the process is: (Take R = 8.3 J/K-mole and suppose there is no atmosphere).
One mole of an ideal gas is kept enclosed under a light piston (area=10– 2 m2 ) connected by a compressed spring (spring constant 100 N/m). The volume of gas is 0.83 m3 and its temperature is 100K. The gas is heated slowly so that it compresses the spring further by 0.1 m. The work done by the gas in the process is: (Take R = 8.3 J/K-mole and suppose there is no atmosphere).
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A rod of length l is sliding such that one of its ends is always in contact with a vertical wall and its other end is always in contact with horizontal surface. Just after the rod is released from rest, the magnitude of acceleration of end points of the rod is a and b respectively. The angular acceleration of rod at this instant will be
A rod of length l is sliding such that one of its ends is always in contact with a vertical wall and its other end is always in contact with horizontal surface. Just after the rod is released from rest, the magnitude of acceleration of end points of the rod is a and b respectively. The angular acceleration of rod at this instant will be
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Physics-
Two sound waves are superimposed. The resulting pressure variation at a single point at a distance 'x' from the source is graphed below :
The beat frequency of the resulting sound wave is :
Two sound waves are superimposed. The resulting pressure variation at a single point at a distance 'x' from the source is graphed below :
The beat frequency of the resulting sound wave is :
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