A sliver wire has mass \((0.6 \pm 0.006) \; g\), radius \((0.5 \pm 0.005) \; mm\) and length \((4 \pm 0.04) \; cm\). The maximum percentage error in the measurement of its density will be \(......\,\%\)

A ball of mass 100 g is projected with velocity \(20 \mathrm{~m} / \mathrm{s}\) at \(60^{\circ}\) with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is

If \(Y, K\) and \(\eta\) are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.

Light enters from air into a given medium at an angle of \(45^{\circ}\) with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of \(15^{\circ}\) from its original direction. The refractive index of the medium is.

A circular coil having \(200\) turns, \(2.5 \times 10^{-4} \mathrm{~m}^2\) area and carrying \(100 \mu \mathrm{A}\) current is placed in a uniform magnetic field of \(1 \mathrm{~T}\). Initially the magnetic dipole moment \((\vec{M})\) was directed along \(\vec{B}\). Amount of work, required to rotate the coil through \(90^{\circ}\) from its initial orientation such that \(\overrightarrow{\mathrm{M}}\) becomes perpendicular to \(\vec{B}\) is _______ \(\mu \mathrm{J}\).

In the circuit shown, the resistance \(r\) is a variable resistance. If for \(r = fR,\)  the heat generation in \(r\) is maximum then the value of \(f\) is 

In a Wheatstone bridge (see figure) Resistance \(P\) and \(Q\) are approximately equal. When \(R = 400\,\Omega ,\) the bridge is balanced. On interchanging \(P\) and \(Q,\) the value of \(R,\) for balance is \(405\,\Omega .\) The value of \(X\) is close to ................. \(ohm\)

The velocity of sound in a gas. in which two wavelengths \(4.08\,m\) and \(4.16\,m\) produce \(40\) beats in \(12\,s\), will be ..............\(ms ^{-1}\)

A nucleus \(A\), with a finite de -broglie wavelength \(\lambda_A\), undergoes spontaneous fission into two nuclei \(B\) and \(C\) of equal mass. \(B\) flies in the same direction as that of \(A\), while \(C\) flies in the opposite direction with a velocity equal to half of that of \(B\). The de -Broglie wavelength \(\lambda_B\) and \(\lambda_C\) of \(B\) and \(C\) are respectively

The position of an object having mass \(0.1\) kg as a function of time \(t\) is given as \(\vec{r} = \left(10t^2\hat{i} + 5t^3\hat{j}\right)\) m. At \(t = 1\) s, which of the following statements are correct?
A. The linear momentum \(\vec{p} = \left(2\hat{i} + 1.5\hat{j}\right)\) kg·m/s.
B. The force acting on the object \(\vec{F} = \left(2\hat{i} + 3\hat{j}\right)\) N.
C. The angular momentum of the object about its origin \(\vec{L} = 15\hat{k}\) J·s.
D. The torque acting on the object about its origin \(\vec{\tau} = 20\hat{k}\) N·m.
Choose the correct answer from the options given below :

A telescope with objective diameter \(R\) is used to observe a distant star emitting light of wavelength \(500\) nm, at a resolution of \(5 \times 10^{-7}\) radian. The value of \(R\) is _____ cm.

A sphere of radius \('a'\) and mass \('m'\) rolls along a horizontal plane with constant speed \(v_{0}\). It encounters an inclined plane at angle \(\theta\) and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel?

In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of \(\left[M^a L^b T^c\right]\). If \(b=-3\), the value of \(c\) is ________