If a rubber ball falls from a height \(h\) and rebounds upto the height of \(h / 2\). The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are _______.

The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of \(7 \times 10^6 \mathrm{~Pa}\), would be ____ \(\mathrm{mm}^3\).
(Given bulk modulus of copper \(=1.4 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}\) )

A body \(A,\) of mass \(m=0.1\; kg\) has an initial velocity of \(3 \hat{\mathrm{i}}\; \mathrm{ms}^{-1} .\) It collides elastically with another body, \(\mathrm{B}\) of the same mass which has an initial velocity of \(5 \hat{\mathrm{j}} \;\mathrm{ms}^{-1}\). After collision. A moves with a velocity \(\overline{\mathrm{v}}=4(\hat{\mathrm{i}}+\hat{\mathrm{j}})\). The energy of \(\mathrm{B}\) after collision is written as \(\frac{\mathrm{x}}{10} \;\mathrm{J}\) The value of \(x\) is

An inductor \((L = 0.03\;H)\) and a resistor \((R = 0.15 k\Omega )\) are connected in series to a battery of \(15\;V\) \(EMF\) in a circuit shown below. The key \(K_1\) has been kept closed for a long time. Then at \(t = 0\), \(K_1\) is opened and key \(K_2\) is closed simultaneously. At \(t = 1 \;ms\), the current in the circuit will be ........... \(mA\). (\({e^5} \cong 150)\)

A solution containing active cobalt \({}_{27}^{60}Co\) having activity of \(0.8\,\mu Ci\) and decay constant \(\lambda \) is injected in an animal's body. If \(1 \,cm^3\) of blood is drawn from the animal's body after \(10\, hrs\) of injection, the activity found was \(300\, decays\) per minute. What is the volume of blood that is flowing in the body?..........\(litres\) ( \(ICi = 3.7 \times 10^{10}\) decay per second and at \(t = 10\, hrs\) \({e^{ - \lambda t}} = 0.84\) )

A bimetallic strip consists of metals \(A\) and \(B\). It is mounted rigidly as shown. The metal \(A\) has higher coefficient of expansion compared to that of metal \(B\). When the bimetallic strip is placed in a cold both, it will :

An \(X-\)ray tube is operated at \(1.24\) million volt. The shortest wavelength of the produced photon will be ..... \(nm\)

A cubical volume is bounded by the surfaces \(x =0, x = a , y =0, y = a , z =0, z = a\). The electric field in the region is given by \(\overrightarrow{ E }= E _0 \times \hat{ i }\). Where \(E _0=4 \times 10^4 NC ^{-1} m ^{-1}\). If \(a =2 cm\), the charge contained in the cubical volume is \(Q \times 10^{-14} C\). The value of \(Q\) is \(...........\) Take \(\left.\varepsilon_0=9 \times 10^{-12} C ^2 / Nm ^2\right)\) 

A solid cylinder of mass \(m\) is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is: [The coefficient of static friction, \(\mu_{ s },\) is \(\left.0.4\right]\)

Two conducting circular loops \(A \) and \(B\) are placed in the same plane with their centres coinciding as shown in figure. The mutual inductance between them is _______.

Given below are two statements: Statement\(-I :\) An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable. Statement\(-II :\) Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed. In the light of the above statements, choose the correct answer from the options given below :

An object is projected in the air with initial velocity \(u\) at an angle \(\theta\). The projectile motion is such that the horizontal range \(R\), is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be \(.......\) degree.