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A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be : ($g = 10 \text{ m/s}^2$)
<p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">pent-2-en-4-yne is</p>
<p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">The speed of a swimmer in still water is</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">20 m/s. The speed of river water is 10 m/s and</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">is flowing due east. If he is standing on the</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">south bank and wishes to cross the river along</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">the shortest path the angle at which he should</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">make his strokes w.r.t. north is given by </p>
<p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;"><span class="s1" style="font-width: normal; line-height: normal; font-family: Symbol; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;">$\alpha$</span>-particle consists of :</p>
A short electric dipole has a dipole moment of $16 \times 10^{-9} C m$. The electric potential due to the dipole at a point at a distance of $0.6 m$ from the centre of the dipole, situated on a line making an angle of $60^{\circ}$ with the dipole axis is : ($\frac{1}{4\pi \epsilon_0} = 9 \times 10^9 N m^2/C^2$)
A screw gauge gives the following readings when used to measure the diameter of a wire. Main scale reading : 0 mm. Circular scale reading : 52 divisions. Given that 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is
A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5 g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is :
The velocity of a small ball of mass $M$ and density $d$, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $\frac{d}{2}$, then the viscous force acting on the ball will be
For the logic circuit shown, the truth table is:
For a plane electromagnetic wave propagating in $x$-direction, which one of the following combination gives the correct possible directions for electric field ($E$) and magnetic field ($B$) respectively?
A series LCR circuit is connected to an ac voltage source. When L is removed from the circuit, the phase difference between current and voltage is $\frac{\pi}{3}$. If instead C is removed from the circuit, the phase difference is again $\frac{\pi}{3}$ between current and voltage. The power factor of the circuit is :
A proton and an $\alpha$-particle both enter a region of uniform magnetic field $B$, moving at right angles to the field. If the radius of circular orbits for both particles is equal and the kinetic energy acquired by the proton is $1\text{ MeV}$, the energy acquired by the $\alpha$-particle will be:
An infinitely long straight conductor carries a current of $5\text{ A}$ as shown. An electron is moving with a speed of $10^5\text{ m/s}$ parallel to the conductor. The perpendicular distance between the electron and the conductor is $20\text{ cm}$ at an instant. Calculate the magnitude of the force experienced by the electron at that instant.
Two conducting circular loops of radii $R_1$ and $R_2$ are placed in the same plane with their centres coinciding. If $R_1 >> R_2$, the mutual inductance $M$ between them will be directly proportional to
For the given circuit, the input digital signals are applied at the terminals $A$, $B$ and $C$. What would be the output at the terminal $y$?
A copper wire of length $10\text{ m}$ and radius $\frac{10^{-2}}{\sqrt{\pi}}\text{ m}$ has electrical resistance of $10\ \Omega$. The current density in the wire for an electric field strength of $10\text{ V/m}$ is
Two charged spherical conductors of radius $R_1$ and $R_2$ are connected by a wire. Then the ratio of surface charge densities of the spheres ($\sigma_1/\sigma_2$) is
A particle of mass '$m$' is projected with a velocity $v = kv_e$ ($k < 1$) from the surface of the earth. ($v_e$ = escape velocity). The maximum height above the surface reached by the particle is
A ball of mass $0.15 \text{ kg}$ is dropped from a height $10 \text{ m}$, strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is ($g = 10 \text{ m/s}^2$) nearly
10 resistors, each of resistance $R$ are connected in series to a battery of emf $E$ and negligible internal resistance. Then those are connected in parallel to the same battery, the current is increased $n$ times. The value of $n$ is