A spherical shell of 1 kg mass and radius R is rolling with angular speed ω on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin O is \(\frac{a}{3}R^2w\). The value of a will be
At time t = 0, a material is composed of two radioactive atoms A and B, where N$_A$(0) = 2N$_B$(0). The decay constant of both kind of radioactive atoms is \(\lambda\). However, A disintegrates to B and B disintegrates to C. Which of the following figures represents the evolution of N$_B$(t)/N$_B$(0) with respect to time t? [ $N_A(0)$ = No. of A atoms at t = 0 ] [ $N_B(0)$ = No. of B atoms at t = 0 ]
A parallel-plate capacitor with plate area A has separation d between the plates. Two dielectric slabs of dielectric constant K\(_1\) and K\(_2\) of same area A/2 and thickness d/2 are inserted in the space between the plates. The capacitance of the capacitor will be given by:
A capacitor of \( 50 \, \mu F \) is connected in a circuit as shown in figure. The charge on the upper plate of the capacitor is \(\dots\dots\dots\) \( \mu C \).
An object is placed at a distance of 12 cm from a convex lens. A convex mirror of focal length 15 cm is placed on other side of lens at 8 cm as shown in the figure. Image of object coincides with the object. When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be __________ (cm).