A parallel beam of light travelling in air (refractive index \(1.0\)) is incident on a convex spherical glass surface of radius of curvature \(50 \, \text{cm}\). Refractive index of glass is \(1.5\). The rays converge to a point at a distance \(x \, \text{cm}\) from the centre of curvature of the spherical surface. The value of \(x\) is ___________.
A Wheatstone bridge is initially at room temperature and all arms of the bridge have same value of resistances \[ (R_1=R_2=R_3=R_4). \] When \(R_3\) resistance is heated, its resistance value increases by \(10%\). The potential difference \((V_a-V_b)\) after \(R_3\) is heated is _______ V.
The heat generated in 1 minute between points A and B in the given circuit, when a battery of 9 V with internal resistance of 1 \(\Omega\) is connected across these points is ______ J.
The strain-stress plot for materials A, B, C and D is shown in the figure. Which material has the largest Young's modulus?
A small bob A of mass m is attached to a massless rigid rod of length 1 m pivoted at point P and kept at an angle of 60° with vertical. At 1 m below P, bob B is kept on a smooth surface. If bob B just manages to complete the circular path of radius R after being hit elastically by A, then radius R is_______ m :
The following diagram shows a Zener diode as a voltage regulator. The Zener diode is rated at \(V_z = 5\) V and the desired current in load is 5 mA. The unregulated voltage source can supply up to 25 V. Considering the Zener diode can withstand four times of the load current, the value of resistor \(R_s\) (shown in circuit) should be_______ \(\Omega\).
A wire of uniform resistance \(\lambda\) \(\Omega\)/m is bent into a circle of radius r and another piece of wire with length 2r is connected between points A and B (ACB) as shown in figure. The equivalent resistance between points A and B is_______ \(\Omega\).
Two point charges 2q and q are placed at vertex A and centre of face CDEF of the cube as shown in figure. The electric flux passing through the cube is :
An object is projected with kinetic energy K from point A at an angle 60° with the horizontal. The ratio of the difference in kinetic energies at points B and C to that at point A (see figure), in the absence of air friction is :
Two short dipoles \( (A, B) \), \( A \) having charges \( \pm 2\,\mu\text{C} \) and length \( 1\,\text{cm} \) and \( B \) having charges \( \pm 4\,\mu\text{C} \) and length \( 1\,\text{cm} \) are placed with their centres \( 80\,\text{cm} \) apart as shown in the figure. The electric field at a point \( P \), equidistant from the centres of both dipoles is \underline{\hspace{2cm}} N/C.