A block of mass \(m\) slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is : Given \({m}=8 \,{kg}, {M}=16\, {kg}\) Assume all the surfaces shown in the figure to be frictionless.

Correct formula for height of a satellite from earths surface is _______.

A parallel plate capacitor with air between the plate has a capacitance of \(15 pF\). The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant \(3.5.\) Then the capacitance becomes \(\frac{ x }{4}\,pF\).The value of \(x\) is \(............\)

The electric field at point p due to an electric dipole is E . The electric field at point R on equitorial line will be \(\frac{E}{x}\). The value of \(x\) is _______.

Identify the correct statements :
A. Electrostatic field lines form closed loops.
B. The electric field lines point radially outward when charge is greater than zero.
C. The Gauss-Law is valid only for inverse-square force.
D. The workdone in moving a charged particle in a static electric field around a closed path is zero.
E. The motion of a particle under Coulomb's force must take place in a plane.
Choose the correct answer from the options given below :

Number of molecules in a volume of \(4\, cm ^{3}\) of a perfect monoatomic gas at some temperature \(T\) and at a pressure of \(2\, cm\) of mercury is close to \(?\) (Given, mean kinetic energy of a molecule (at \(T\) ) is \(4 \times 10^{-14}\) erg, \(g=980\, cm / s ^{2}\), density of mercury \(=13.6\, g / cm ^{3}\))

A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of \(10 \,m\) in \(t \;s ,\) the distance travelled by the toy in the next \(t s\) will be .........\(m\)

The magnetic field in a region is given by \(\overrightarrow{ B }= B _{0}\left(\frac{ x }{ a }\right) \,\hat{ k }\). A square loop of side \(d\) is placed with its edges along the \(x\) and \(y\) axes. The loop is moved with a constant velocity \(\overrightarrow{ v }= v _{0} \hat{ i }\). The emf induced in the loop is:

Heat energy of \(184\,kJ\) is given to ice of mass \(600\,g\) at \(-12^{\circ}\,C\), Specific heat of ice is \(2222.3\,J\,kg ^{-1^{\circ}}\,C ^{-1}\) and latent heat of ice in \(336\,kJ / kg ^{-1}\) \((A)\) Final temperature of system will be \(0^{\circ} C\). \((B)\) Final temperature of the system will be greater than \(0^{\circ} C\). \((C)\) The final system will have a mixture of ice and water in the ratio of \(5: 1\). \((D)\) The final system will have a mixture of ice and water in the ratio of \(1: 5\). \((E)\) The final system will have water only. Choose the correct answer from the options given below:

What will be the nature of flow of water from a circular tap, when its flow rate increased from \(0.18\, L / min\) to \(0.48\, L / min\) ? The radius of the tap and viscosity of water are \(0.5\, cm\) and \(10^{-3}\, Pa s\), respectively. (Density of water : \(10^{3}\, kg / m ^{3}\) )