Physics

A square shaped hole of side l = a/2 is carved out at a distance d = a/2 from the centre O of a uniform circular disk of radius a. If the distance of the centre of mass of the remaining portion from O is -a/X, value of X (to the nearest integer) is :

A wire of density 9 * 10⁻³ kg cm⁻³ is stretched between two clamps 1 m apart. The resulting  strain in the wire is 4.9 * 10⁻⁴. The lowest frequency of the transverse vibrations in the wire (Young's modulus of wire Y = 9 * 10¹⁰ Nm⁻²), (to the nearest integer), is

A light ray enters a solid glass sphere of refractive index μ = √3 at an angle of incidence 60°. The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degrees) between the reflected and refracted rays at this surface is

An ideal cell of emf 10 V is connected in circuit shown in figure. Each resistance is 2Ω. The potential difference (in V) across the capacitor when it is fully charged is

A potentiometer wire PQ of 1 m length is connected to a standard cell E₁. Another cell E₂ of emf 1.02 V is connected with a resistance 'r' and switch S (as shown in figure). With switch S open, the null position is obtained at a distance of 49 cm from Q. The potential gradient in the potentiometer wire is:

In a plane electromagnetic wave, the directions of electric field and magnetic field are represented by k̂ and 2î – 2ĵ, respectively. What is the unit vector along direction of propagation of the wave.

A small point mass carrying some positive charge on it, is released from the edge of a table. There is a uniform electric field in this region in the horizontal direction. Which of the following options then correctly describe the trajectory of the mass? (Curves are drawn schematically and are not to scale)

If momentum (P), area (A) and time (T) are taken to be the fundamental quantities, then the dimensional formula for energy is :

A heat engine is involved with exchange of heat of 1915 J, –40 J, +125 J and –QJ, during one cycle achieving and efficiency of 50.0%. The value of Q is: