An object is at a distance of \(20\,m\) from a convex lens of focal length \(0.3\,m.\) The lens forms an image of the object. If the object moves away from the lens at a speed of \(5\,m/s,\) the speed and direction of the image will be

From the given data, the amount of energy required to break the nucleus of aluminium \({ }_{13}^{27} {Al}\) is \(....\,x \times 10^{-3} {J}\) Mass of neutron \(=1.00866 \,{u}\) Mass of proton \(=1.00726 \,{u}\) Mass of aluminium nucleus \(=27.18846\, {u}\) (Assume \(1\,u\) corresponds to \(x\,J\) of energy) (Round off to the nearest integer)

A mass \(M\) hangs on a massless rod of length \(l\) which rotates at a constant angular frequency. The mass \(M\) moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular velocity \(\omega .\) The angular momentum of \(M\) about point \(A\) is \(L _{ A }\) which lies in the positive \(z\) direction and the angular momentum of \(M\) about \(B\) is \(L _{ B }\). The correct statement for this system is

A satellite is in an elliptical orbit around a planet \(P.\) It is observed that the velocity of the satellite when it is farthest from the planet is \(6\) time less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is\(......\)

A spherical surface of radius of curvature \(R\), separates air from glass (refractive index \(=1.5\) ). The centre of curvature is in the glass medium. A point object ' \(O\) ' placed in air on the optic axis of the surface, so that its real image is formed at ' \(I\) ' inside glass. The line OI intersects the spherical surface at P and \(\mathrm{PO}=\mathrm{PI}\). The distance PO equals to ________.

Two identical thin metal plates has charge \(q _{1}\) and \(q _{2}\) respectively such that \(q _{1}> q _{2}\). The plates were brought close to each other to form a parallel plate capacitor of capacitance \(C\). The potential difference between them is.

A cell \(E _{1}\) of \(emf 6 V\) and internal resistance \(2 \Omega\) is connected with another cell \(E _{2}\) of \(emf 4 V\) and internal resistance \(8 \Omega\) (as shown in the figure). The potential difference across points \(X\) and \(Y\) is............ \(V\)

A current of \(2\, mA\) was passed through an unknown resistor which dissipated a power of \(4.4\, W\). Dissipated power when an ideal power supply of \(11\, V\) is connected across it is

Three parallel plate capacitors each with area A and separation d are filled with two dielectric ( \(k _1\) and \(k _2\) ) in the following fashion. Which of the following is true? \(\left( k _1> k _2\right)\)

Match List - I with List - II.

List - I	List - II
(A) Electric field inside (distance \(r>0\) from center) of a uniformly charged spherical shell with surface charge density \(\sigma\), and radius R.	(I) \(\sigma / \epsilon_0\)
(B) Electric field at distance \(r >0\) from a uniformly charged infinite plane sheet with surface charge density \(\sigma\).	(II) \(\sigma / 2 \epsilon_0\)
(C) Electric field outside (distance \(r>0\) from center) of a uniformly charged spherical shell with surface charge density \(\sigma\), and radius R.	(III) \(0\)
(D) Electric field between 2 oppositely charged infinite plane parallel sheets with uniform surface charge density \(\sigma\).	(IV) \(\frac{\sigma R^2}{\epsilon_0 r^2}\)

Choose the correct answer from the options given\(\text{ }\)below\(\text{ }\):

A balloon and its content having mass \(M\) is moving up with an acceleration ' \(a\) '. The mass that must be released from the content so that the balloon starts moving up with an acceleration ' \(3 a^{\prime}\) will be
(Take ' g ' as acceleration due to gravity)

A nucleus has mass number \(A_1\) and volume \(V_1\). Another nucleus has mass number \(A_2\) and volume \(V_2\). If relation between mass number is \(A_2=4 A_1\), then \(\frac{V_2}{V_1}=\)_______.