The straight wire AB carries a current \(I\). The ends of the wire subtend angles \(\theta_1\) and \(\theta_2\) at the point \(P\) as shown in the figure. The magnetic field at the point \(P\) is:
In the given circuit, \(E_1 = E_2 = E_3 = 2V\) and \(R_1 = R_2 = 4\Omega\), then the current flowing through the branch AB is:
A particle is moving in a straight line. The variation of position $ x $ as a function of time $ t $ is given as: $ x = t^3 - 6t^2 + 20t + 15 $. The velocity of the body when its acceleration becomes zero is:
A force of \( F = 0.5 \) N is applied on the lower block as shown in the figure. The work done by the lower block on the upper block for a displacement of 3 m of the upper block with respect to the ground is (Take, \( g = 10 \) m/s\( ^2 \)):
An ideal massless spring \( S \) can be compressed \( 1 \) m by a force of \( 100 \) N in equilibrium. The same spring is placed at the bottom of a frictionless inclined plane inclined at \( 30^\circ \) to the horizontal. A \( 10 \) kg block \( M \) is released from rest at the top of the incline and is brought to rest momentarily after compressing the spring by \( 2 \) m. If \( g = 10 \) m/s\( ^2 \), what is the speed of the mass just before it touches the spring?
A gas can be taken from A to B via two different processes ACB and ADB. When path ACB is used, \( 60 J \) of heat flows into the system and \( 30 J \) of work is done by the system. If path ADB is used, the work done by the system is \( 10 J \). The heat flow into the system in path ADB is:
A plane progressive wave is given by y = 2 cos 2pi (330t - x) m. The frequency of the wave is:}