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The resistance of the rod is 1 Ω. It is bent in form of a square. What is the resistance across adjacent corners?
When the rod is bent in the form of a square, then each side has a resistance of 1/4 Ω. As shown R1, R2 and R3 are connected in series, so, their equivalent resistance,
Figure shows the vertical cross-section of a vessel filled with a liquid of density ρ. The normal thrust per unit area on the walls of the vessel at point P, as shown will be
Depth of point P from the free surface of water in the vessel = (H − h). Since, the liquid exerts equal pressure in all direction at one level, hence, the pressure at P = (H − h)ρg
A conducting ring of mass 2 kg and radius 0.5 m is placed on a smooth horizontal plane. The ring carries a current i = 4 A. A horizontal magnetic field B = 10 T is switched on at time t = 0 as shown in the figure. The initial angular acceleration of the ring will be
A stone is dropped from a height of 45 m on a horizontal level ground. There is the horizontal wind blowing due to which horizontal acceleration of the stone becomes 10 m s−2. (Take g = 10 m s−2). The time taken (t)t by stone to reach the ground and the net horizontal displacement (x) of the stone from the time it is dropped and till it reaches the ground are respectively
The current (I) in the inductance is varying with time according to the plot shown in the figure.
The correct variation of voltage with time in the coil is
From the graph given in the question, we can see that the current is rising up to the time T/2 from 0, and decaying up to the time T from T/2.
Now, voltage induced in an inductor is given as;
If we see the slope for up to t = T/2 i.e; dIdtdIdt is positive and constant (L is already constant term) which shows that the value of voltage is not changing from time t = 0 to t = T/2.
And again, if we see the slope for up to t = T i.e; dI/dt is negative but constant which shows that the value of voltage is not changing from time t= T/2 to t = T.
Hence, the graph between voltage and time is as shown below;
Two charges q1 and q2 are placed 30 cm apart, as shown in the figure. A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is where k is
A point source of heat of power P is placed at the centre of a spherical shell of mean radius R. The material of the shell has thermal conductivity K. Calculate the thickness of the shell if the temperature difference between the outer and inner surfaces of the shell in steady-state is T.
Consider a concentric spherical shell of radius r and thickness dr as shown in diagram. The radial rate of flow of heat through this shell in steady state will be,
Now in steady state as no heat is absorbed, rate of loss of heat by conduction is equal to that of supply, i.e., H = P, and here
θ1 - θ2 = T and a ≃ b = Ra ≃ b = R
So Equation (i) becomes,
Two condensers, one of capacity C and other of capacity C/2 are connected to a V - volt battery, as shown in the figure. The work done in charging fully both the condensers is
As the condensers are connected in parallel, therefore potential difference across both the condensers remains the same.
Two radio antennas radiating waves in phase are located at points A and B, 200 m apart (Figure). The radio waves have a frequency of 6 MHz. A radio receiver is moved out from point BB along a line perpendicular to the line connecting A and B (line BC as shown in the figure). At what distances from B will there be destructive interference?
With the assumption of no slipping, determine the mass mm of the block which must be placed on the top of a 6 kg cart in order that the system period is 0.75 s. What is the minimum coefficient of static friction μS for which the block will not slip relative to the cart if the cart is displaced m50 mm from the equilibrium positions and released? Take (g = 9.8 m s-2).
= 2.55 kg
Maximum acceleration of SHM is,
amax = ω2A (A = amplitude)
i.e., maximum force on mass 'm' is m ω2 A which is being provided by the force of friction between the mass and the cart. Therefore,
μsmg ≥ mω2 A
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