A simple pendulum with a solid metal bob has a period T. The metal bob is now immersed in a liquid having density one-tenth that of the metal of the bob. The liquid is non-viscous. Now the period of the same pendulum with its bob remaining all the time in the liquid will be
If the earth is supposed to be a sphere of radius R, \[g30{}^\circ \] is the value of acceleration due to gravity at latitude of \[30{}^\circ \] and g at the equator, the value of g- \[g30{}^\circ \] is -
A particle of mass m and charge q enters a region of magnetic field (as shown) with speed v at t = 0. There is a region in which the magnetic field is absent as shown. The particle after entering the region collide elastically with a rigid wall. Time t after which the velocity of particle become antiparallel to its initial velocity is -
A magnet is suspended horizontally in the earth's magnetic field. When it is displaced and released, it oscillates in a horizontal plane with a period T. If a piece of wood of same M.I as the magnet is attached to the magnet is attached to the magnet, the new period of oscillation of the system would be -
Two identical conducting ring A and B of radius R are in pure rolling over a horizontal conducting plane with same speed (of center of mass) v but in opposite direction. A constant magnetic field B is present pointing inside the plane of paper. Then the potential difference between the highest points of the two rings, is:
Two carnote engines A and B have their sources at 1000 K and 1100 K and their sinks are at 400 K and 500 K respectively. If \[{{\eta }_{A}}\] and \[{{\eta }_{B}}\] are their efficiencies,
A meter scale is balanced at its mid-point if a 20N weight is balanced at 20 cm mark and a 30 N weight is hanged at x cm mark. Calculate the value of x.
Two waves are given by \[{{y}_{1}}=a\,sin(\omega t-kx)\]and \[{{y}_{2}}=a\,cos\left( \omega t-kx \right)\]. The phase difference between the two waves is-
An observer moves towards a stationary source of sound of frequency n. The apparent frequency heard by him is 2n. If the velocity of sound in air is 332 m/sec, then the velocity of the observer is-
A pi-mesic hydrogen atom is a bound state of a charged pion (denoted by\[{{\pi }^{-}},{{m}_{{{\pi }^{-}}}}=273{{m}_{e}}\]) and a proton.. The number of revolution a \[{{\pi }^{-}}\] makes in ground state of atom before it decays (mean life of a\[{{\pi }^{+}}\simeq {{10}^{-8}}S\])
\[{{M}_{x}}\] and \[{{M}_{y}}\] denote the atomic masses of the parent and the daughter nuclei respectively in a radioactive decay. The Q-value for a \[{{\beta }^{-}}\]-decay is \[{{Q}_{1}}\] and that for a \[{{\beta }^{+}}\]-decay is Ch. If me denotes the mass of an electron, the which of the following statements is correct -
An e.m. wave of wavelength\[\lambda \], is incident on a photosensitive surface of negligible work function. If the photoelectrons emitted from this surface have the de Broglie wavelength \[{{\lambda }_{1}}\], then \[\lambda \]=
A particle A with a mass ma is moving with a velocity v and hits a particle B (mass ms) at rest (one dimensional motion). Find the change m the de Broglie wavelength of the particle A. Treat the collision as elastic -
A point charge q is situated at a distance d from one end of a thin non-conducting rod of length L having a charge Q distributed uniformly along its length. The magnitude of the electric force between them will be -
Two square metallic plates of side a = 1 m are kept at d = 8.85 mm apart, like a parallel plate capacitor, in such a way that their surfaces are normal to the oil surface in a tank filled with insulating oil (K = 11). The plates are connected to a battery of emf V = 500 volt as shown in figure. The plates are then lowered vertically into the oil at a speed of\[\text{V}={{10}^{-3}}m{{s}^{-1}}\]. Neglecting resistance of connecting wires, calculate the current drawn from battery during the process (so\[{{\varepsilon }_{0}}=8.85\times {{10}^{-12}}{{C}^{2}}{{N}^{-1}}m{{~}^{-2}}\])
A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first 2 sec, it rotates through an angle\[{{\theta }_{1}}\]; in the next 2 sec, it rotates through an additional angle\[{{\theta }_{1}}\]. The ratio of \[{{\theta }_{1}}/{{\theta }_{2}}\] is?
Consider the situation shown in figure. The system is released from rest and the block of mass 1.0 kg is found to have a speed 0.3 m/s after it has descended through a distance of 1 m. Find the coefficient of kinetic friction between the block and the table.
An object is projected with a speed 10 m/s at an angle of \[30{}^\circ \] with the horizontal. The object breaks down into n equal fragments during its motion. One fragment is found to strike the ground at a distance of \[\sqrt{3}\] m from the point of projection in the same azimuthal plane, in which the object is projected. If the centre of mass of the remaining fragments strikes the ground at distance of \[7\sqrt{3}\,m\] from the point of projection, then the value of n is (all parts fall simultaneously on grounds)
A rigid body can be hinged about any point on the x - axis. When it is hinged such that the hinge is at x, the moment of inertia is given by\[I=2{{x}^{2}}-12x+27\]. Find the x coordinate of centre of mass.
A complex of a certain metal ion has a magnetic moment of 4.90 BM. Another complex of the same metal ion in the same oxidation state has a zero magnetic moment. The central metal ion could be which of the following?
For a gas containing \[{{10}^{23}}\] molecules (each having mass \[{{10}^{-22}}g\]) in a volume of \[1\text{ }d{{m}^{3}},\] the root mean square speed \[({{\mu }_{rms}})\] is \[{{10}^{5}}cm\,{{s}^{-1}}\]. Calculate the total kinetic energy of molecules and gas temperature. (Boltzmann constant, \[=1.38\times {{10}^{-23}}J{{K}^{-1}}\])
One mole of an ideal gas undergoes a reversible Carnot cycle with \[{{V}_{1}}=20L,\]\[{{V}_{2}}=40L,\] and \[{{T}_{1}}=300K\]. Let \[{{T}_{2}}=200K,\]\[{{C}_{v.m}}=(3/2)R.\] \[\Delta U\]and \[\Delta V\] for adiabatic reversible compression are, respectively,
Consider the following reaction \[{{N}_{2}}(g)+3{{H}_{2}}(g)2N{{H}_{3}}(g);\,{{K}_{1}}\] \[{{N}_{2}}(g)+{{O}_{2}}(g)2O(g);\,{{K}_{2}}\] \[{{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g){{H}_{2}}O(g);\,{{K}_{3}}\] The equilibrium constant for \[2N{{H}_{3}}(g)+\frac{5}{2}{{O}_{2}}(g)2NO(g)+3{{H}_{2}}O(g)\] will be-
Three compounds , , and are given. Select the INCORRECT statement.
A)
The rate of catalytic hydrogenation is faster in than in and
doneclear
B)
The rate of catalytic hydrogenation is faster in than in .
doneclear
C)
has a cyclopropene ring whose strain on going to less strained cyclopropane ring is reduced on hydrogenation. Similarly, cyclobutene ring in on hydrogenation is reduced to less-strained cyclobutane ring. But cyclopropene ring is more strained than cyclobutene ring, so faster hydrogenation is in than in .
doneclear
D)
There is a little change in the ring strain when the cyclohexene ring is reduced.
An aromatic compound , \[{{C}_{8}}{{H}_{10}},\] on oxidation with acidic \[KMn{{O}_{4}}\] gives dibasic acid. The compound on nitration gives three isomeric nitro derivatives. The compound is
A diatomic molecule has\[u=1.2\text{ }D\]. Its bond distance is\[1.0\text{ }\overset{o}{\mathop{A}}\,\]. The percent of fraction of electronic charge exists on each atom is _______.
\[KMn{{O}_{4}}\] reacts with \[N{{a}_{2}}{{S}_{2}}{{O}_{3}}\] in acidic, strongly basic and aqueous (neutral) medium. \[100\text{ }mL\]of \[KMn{{O}_{4}}\] reacts with \[100\text{ }mL\]of\[~0.1\text{ }M\] \[N{{a}_{2}}{{S}_{2}}{{O}_{3}}\]in acidic, basic and neutral medium. The sum of molarity (M) of \[KMn{{O}_{4}}\] in acidic, basic and neutral medium is _______.
The amount of ice that will separate out on cooling containing \[50\text{ }g\]of ethylene glycol in \[200\text{ }g\]of water to \[-10.0{}^\circ C\]in g is _______. (\[{{K}_{f}}\]for water\[=1.86\text{ }K\text{ }mo{{l}^{-1}}\text{ }kg\])
A function has a second order derivatives . If its graph passes through the point (2, 1) and at that point the tangent to the graph is , then the function is
The point P is the intersection of the straight line joining the points 0(2, 3, 5) and R(1, -1, 4) with the plane . If S is the foot of the perpendicular drawn from the point to QR, then the length of the line segment PS is
If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number
If a flagstaff of 6 metres high placed on the top of a tower throws a shadow of metres along the ground, then the angle (in degrees) that the sun makes with the ground is