A uniform rod of mass 20 kg and length 5 m leans against a smooth vertical wall making an angle of with it. The other end rests on a rough horizontal floor. The friction force that the floor exerts on the rod is (take ).
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A uniform rod of mass 20 kg and length 5 m leans against a smooth vertical wall making an angle of with it. The other end rests on a rough horizontal floor. The friction force that the floor exerts on the rod is (take ).
A bob of heavy mass is suspended by a light string of length . The bob is given a horizontal velocity as shown. If the string gets slack at some point making an angle from the horizontal, the ratio of the speed of the bob at point to its initial speed is:

Consider a water tank shown in the figure. It has one wall at and is very wide in the -direction. When filled with a liquid of surface tension and density , the liquid surface makes a small angle with the -axis at . If is the height of the surface, the equation for is:
(take , is the acceleration due to gravity)
The electric field in a plane electromagnetic wave is given by . Then expression for the corresponding magnetic field is (here subscripts denote the direction of the field):
The current passing through the battery in the given circuit is:

A wire of resistance is cut into equal pieces. From these pieces two equivalent resistances are made by adding four of these together in parallel. Then these two sets are added in series. The net effective resistance of the combination is:
A particle of mass is moving around the origin with a constant force pulling it towards the origin. If Bohr model is used to describe its motion, the radius of the th orbit and the particle's speed in the orbit depend on as
A ball of mass kg is dropped from a height of m. The ball hits the ground and rises to a height of m. The impulse imparted to the ball during its collision with the ground is (Take )
A pipe open at both ends has a fundamental frequency in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to:
Two identical point masses and , suspended from two separate massless springs of spring constants and , respectively, oscillate vertically. If their maximum speeds are the same, the ratio of the amplitude of mass to the amplitude of mass is:
The Sun rotates around its centre once in 27 days. What will be the period of revolution if the Sun were to expand to twice its present radius without any external influence? Assume the Sun to be a sphere of uniform density.
The kinetic energies of two similar cars A and B are and respectively. On applying brakes, car A stops after and car B stops after . If and are the magnitudes of the braking forces on cars A and B, respectively, then the ratio is:
The plates of a parallel plate capacitor are separated by . Two slabs of different dielectric constants and with thicknesses and , respectively, are inserted between the plates. Due to this, the capacitance becomes two times larger than when there is nothing between the plates. If , the value of is:
An electric dipole with dipole moment is aligned with the direction of a uniform electric field of magnitude . The dipole is then rotated through an angle of with respect to the electric field. The change in the potential energy of the dipole is:
A constant voltage of is maintained between the points and of the circuit shown in the image. The current through the branch of the circuit is:

A sphere of radius is cut from a larger solid sphere of radius as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the -axis is:

In some appropriate units, the time and position relation of a moving particle is given by . The acceleration of the particle is:
Three identical heat conducting rods are connected in series as shown in the figure. The rods on the sides have thermal conductivity while that in the middle has thermal conductivity . The left end of the combination is maintained at temperature and the right end at . The rods are thermally insulated from outside. In steady state, temperature at the left junction is and that at the right junction is . The ratio is:

Two gases and are filled at the same pressure in separate cylinders with movable pistons of radii and , respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure, the pistons are displaced by and , respectively. If the change in their internal energy is the same, then the ratio is equal to:
A physical quantity is related to four observations , , and as follows: . The percentage errors of measurement in , , and are , , and respectively. The percentage error in the quantity is: