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Two similar thin equi-convex lenses, of focal length $f$ each, are kept coaxially in contact with each other such that the focal length of the combination is $F_1$. When the space between the two lenses is filled with glycerine (which has the same refractive index ($\mu = 1.5$) as that of glass) then the equivalent focal length is $F_2$. The ratio $F_1 : F_2$ will be :
A transverse wave propagating along the $x$-axis is represented by: $y(x,t) = 8.0\sin(0.5\pi x - 4\pi t - \frac{\pi}{4})$, where $x$ is in meters and $t$ in seconds. The speed of the wave is:
A small steel ball of radius $r$ is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta$. After some time, the velocity of the ball attains a constant value known as terminal velocity $v_T$. The terminal velocity depends on the mass of the ball $m$, $\eta$, $r$, and acceleration due to gravity $g$. Which of the following relations is dimensionally correct?
Dimensions of coefficient of viscosity are
A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is : ($\alpha_{Cu} = 1.7 \times 10^{-5}$ K$^{-1}$ and $\alpha_{Al} = 2.2 \times 10^{-5}$ K$^{-1}$)
For Young's double-slit experiment, two statements are given below: Statement I: If screen is moved away from the plane of slits, angular separation of the fringes remains constant. Statement II: If the monochromatic source is replaced by another monochromatic source of larger wavelength, the angular separation of fringes decreases.
Dimensions of stress are:
Whose dimensions are $ML^2T^{-1}$?
Which of the following is not equal to a watt?
If the dimensions of a physical quantity are given by $[M^a L^b T^c]$, then the physical quantity will be:
Young's modulus of a material has the same units as:
A particle of mass $4M$ at rest splits into two particles of mass $M$ and $3M$. The ratio of the kinetic energies of mass $M$ and $3M$ would be:
A sphere of mass $m$ is tied to the end of a string of length $l$ and rotated through the other end along a horizontal circular path with speed $v$. The work done by the centripetal force in a full horizontal circle is:
The potential energy of a certain spring when stretched through a distance 'S' is $10 \text{ joule}$. The amount of work (in joule) that must be done on this spring to stretch it through an additional distance 'S' will be:
Which of the following pair does not have similar dimensions?
If force ($F$), velocity ($v$) and time ($T$) are taken as fundamental units, then the dimensions of mass are
The area of a rectangular field (in $\text{m}^2$) of length $55.3$ m and breadth $25$ m after rounding off the value, for correct significant digits is:
The density of material in the CGS system of units is $4\text{ g/cm}^3$. In a system of units in which unit of length is $10\text{ cm}$ and unit of mass is $100\text{ g}$, the value of density of material in this system will be:
An engine pumps water continuously through a hose. Water leaves the hose with a velocity $v$ and $m$ is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?
A gravitational field is present in a region, and a mass is shifted from $A$ to $B$ through different paths as shown. If $W_1$, $W_2$ and $W_3$ represent the work done by the gravitational force along their respective paths, then: