Let [ε_{0}] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then
[ε_{0}] = [M^{-1}L^{-3}T^{2}A]
[ε_{0}] = [M^{-1}L^{-3}T^{4}A^{2}]
[ε_{0}] =[M^{-2}L^{2}T^{-1}A^{-2}]
[ε_{0}] = [M^{-1}L^{2}T^{-1}A^{2}]
B.
[ε_{0}] = [M^{-1}L^{-3}T^{4}A^{2}]
From Coulomb's Law, F
On Substituting the units, we get
A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density σ at the equilibrium position. The extension x_{0} of the spring when it is in equilibrium is
C.
At equilibrium ΣF = 0
A metallic rod of length ‘l’ is tied to a string of length 2l and made to rotate with angular speed ω on a horizontal table with one end of the string fixed. If there is a vertical magnetic field ‘B’ in the region, the e.m.f. induced across the ends of the rod is
D.
This question has Statement I and Statement II. Of the four choices given after the Statements, choose the
one that best describes the two Statements.
Statement – I: A point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as f
Statement – II : Maximum energy loss occurs when the particles get stuck together as a result of the collision.
Statement – I is true, Statement – II is true, Statement – II is a correct explanation of Statement – I.
Statement – I is true, Statement – II is true, Statement – II is not a correct explanation of Statement – I.
Statement – I is true, Statement – II is false.
Statement – I is false, Statement – II is true
D.
Statement – I is false, Statement – II is true
Before collision, the mass is m and after collision, the mass is m+M
therefore, Maximum energy loss
=
A projectile is given an initial velocity of where is along the ground and is along the vertical. If g = 10 m/s^{2}, the equation of its trajectory is:
y = x-5x2
y = 2x-5x^{2}
4y = 2x- 5x^{2}
4y = 2x-25x^{2}
B.
y = 2x-5x^{2}
Initial velocity,
Magnitude of velocity,
the equation of trajectory of the projectile
The above p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat extracted from the source in a single cycle is
p_{o}v_{o}
4p_{o}v_{o}
B.
Heat is extracted from the source in path DA and AB is
The amplitude of a damped oscillator decreases to 0.9 times its original magnitude is 5s. In another 10s it will decrease to α times its original magnitude, where α equals
0.7
0.81
0.729
0.6
C.
0.729
Amplitude of damped oscillator
What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?
5GmM/6R
2GmM/3R
GmM/2R
GmM/3R
A.
5GmM/6R
From conservation of energy,
Total energy at the planet = Total energy at the altitude
In its orbit the necessary centripetal force provided by gravitational force.
∴
A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1 %. What is the fundamental frequency of steel if density and elasticity of steel are 7.7 × 10^{3} kg/m^{3} and 2.2 × 10^{11}N/m^{2} respectively?
188.5 Hz
178.2 Hz
200.5 Hz
770 Hz
B.
178.2 Hz
A hoop of radius r and mass m rotating with an angular velocity ω_{0}
is placed on a rough horizontal surface.The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?
rω_{0}/4
rω_{0}/3
rω_{0}/2
rω_{0}
C.
rω_{0}/2
From conservation of angular momentum about any fixed point on the surface
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