A particle is executing Simple Harmonic Motion \((SHM)\). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be

person trying to lose weight by burning fat lifts a mass of \(10\ kg\) upto a height of \(1\ m\) \(1000\) times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies \(3.8 \times 10^7\ J\) of energy per kg which is converted to mechanical energy with a \(20\%\) efficiency rate. Take \(g=9.8\) \(ms^{-2}\) 

The internal energy of a monoatomic gas is 3 nRT . One mole of helium is kept in a cylinder having internal cross section area of \(17 cm^2\) and fitted with a light movable frictionless piston. The gas is heated slowly by suppling 126 J heat. If the temperature rises by \(4^{\circ} C\), then the piston will move ___________ cm.
(atmospheric pressure \(=10^5 Pa\) )

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field.
Reason (R) : In absence of an external electric field, the different permanent dipoles of a polar dielectric substance are oriented in random directions.
In the light of the above statements, choose the most appropriate answer from the options given below :

Select the correct statement from the following

A particle starts moving from time \(t=0\) and its coordinate is given as \(x(t)=4t^{3}-3t.\)
A. The particle returns to its original position (origin) 0.866 units later
B. The particle is 1 unit away from origin at its turning point.
C. Acceleration of the particle is non-negative.
D. The particle is 0.5 units away from origin at its turning point.
E. Particle never turns back as acceleration is non-negative.
Choose the correct answer from the options given below :

Two transparent media having refractive indices \(1.0\) and \(1.5\) are separated by a spherical refracting surface of radius of curvature \(30\,cm\). The centre of curvature of surface is towards denser medium and a point object is placed on the principle axis in rarer medium at a distance of \(15\,cm\) from the pole of the surface. The distance of image from the pole of the surface is .......\(cm\)

A microwave of wavelength \(2.0 \mathrm{~cm}\) falls normally on a slit of w1dth \(4.0 \mathrm{~cm}\). The angular spread of the central maxima of the diffraction pattern obtained on a screen \(1.5 \mathrm{~m}\) away from the slit, will be _______.

A series \(LCR\) circuit driven by \(300\, {V}\) at a frequency of \(50 \,{Hz}\) contains a resistance \({R}=3 \,{k} \Omega\), an inductor of inductive reactance \(X_{L}=250 \,\pi \Omega\) and an unknown capacitor. The value of capacitance to maximize the average power should be : (Take \(\pi^{2}=10\) ) (in \(\mu {F}\))

A \(100\,m\) long wire having cross-sectional area \(6.25 \times 10^{-4}\,m ^2\) and Young's modulus is \(10^{10}\,Nm ^{-2}\) is subjected to a load of \(250\,N\), then the elongation in the wire will be :

The colour coding on a carbon resistor is shown in the given figure. The resistance value of the given resistor is:

A heat engine operates between a cold reservoir at temperature \({T}_{2}=400\, {K}\) and a hot reservoir at temperature \({T}_{1} .\) It takes \(300 \,{J}\) of heat from the hot reservoir and delivers \(240\, {J}\) of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be \(....{K}\)