If \(10^{22}\) gas molecules each of mass \(10^{-26}\) kg collide with a surface (perpendicular to it) elastically per second over an area \(1\,\,m^2\) with a speed \(10^4\) m/s, the pressure exerted by the gas molecules will be of the order of:
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\(10^8 \frac{N}{m^2}\)
\(10^3 \frac{N}{m^2}\)
\(10^4 \frac{N}{m^2}\)
\(10^{16}\frac{N}{m^2}\)
Non of the above
A particle moves in one dimension from rest under the influence of a force that varies with the distance traveled by that varies with the distance traveled by the particle as shown in the figure. The kinetic energy of the particle after it has traveled 3 m is:
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\(2.5\,J\)
\(4\,J\)
\(5\,J\)
\(6.5\,J\)
An upright object is placed at a distance of \(40\) cm in front of a convergent lens of focal length \(20\) cm. A convergent mirror of focal length \(10\) cm is placed at a distance of \(60\) cm on the other side of the lens. The position and size of the final image will be:
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\(40\) cm from the convergent mirror, same size as the object
\(20\) cm from the convergent mirror, same size as the object
\(40\) cm from the convergent lens, twice the size of the object
\(20\) cm from the convergent mirror, twice the size of the object
Non of the above
Four particles \(A,B,C\) and \(D\) with masses \(m_A=m,\,m_B=2m,\,m_c=3m \) and \( m_D=4m\) are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is:
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\( \frac{a}{5}\left ( \hat{i}-\hat{j} \right )\)
zero
\( \frac{a}{5}\left ( \hat{i}+\hat{j} \right )\)
\( {a}\left ( \hat{i}+\hat{j} \right )\)
Two identical beakers \(A\) and \(B\) contain equal volumes of two different liquids at \(60^\circ\,C\) each and left to cool down. Liquid in \(A\) has density of \(8\times 10^2\,kg/m^3\) and specific heat of \(2000\,Jkg^{-1}K^{-1}\) while liquid in \(B\) has density of \(10^3kgm^{-3}\) and specific heat of \(4000\,JKg^{-1}K^{-1}\) . Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same)
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A thin strip \(10\) cm long is on a U shaped wire of negligible resistance and it is connected to a spring of spring constant \(0.5Nm^{-1}\) (see figure). The assembly is kept in a uniform magnetic field of \(0.1\,\,T\). If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of \(e\) is \(N\) . If the mass of the strip is \(50\) grams, its resistance \(10\Omega\) and air drag negligible, \(N\) will be close to:
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\(50000\)
\(10000\)
\(1000\)
\(5000\)
A \(20\) Henry inductor coil is connected to a \(10\) ohm resistance in series as shown in figure. The time at which rate of dissipation of energy (Joule’s heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor, is
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\(\frac{2}{ln\,2}\)
\(ln\,2\)
\(\frac{1}{2}\,ln\,2\)
\(2\,ln\,2\)
A wire of length \(2L\) is made by joining two wires \(A\) and \(B\) of same lengths but different radii \(r\) and \(2r\) and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire \(A\) is \(p\) and that in \(B\) is \(q\) then the ratio \(p:q\) is:
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\(1:4\)
\(1:2\)
\(3:5\)
\(4:9\)
A steel wire having a radius of \(2.0\) mm, carrying a load of \(4\) kg, is hanging from a ceiling. Given that \(g=3.1\pi ms^{-2}\) , what will be the tensile stress that would be developed in the wire?
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\(6.2\times 10^6Nm^{-2}\)
\(4.8\times 10^6Nm^{-2}\)
\(5.2\times 10^6Nm^{-2}\)
\(3.1\times 10^6Nm^{-2}\)
Voltage rating of a parallel plate capacitor is \(500V\). Its dielectric can withstand a maximum electric field of \(10^6\,\frac{V}{m}\) . The plate area is \(10^{-4}m^2\) . What is the dielectric constant if the capacitance is \(15\, \,pF\)? (given \( \epsilon _0=8.86\times 10^{-12}C^2/Nm^2\) )
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\(3.8\)
\(6.2\)
\(4.5\)
\(8.5\)
An alternating voltage \( v(t)=220\,sin100\pi l\) volt is applied to a purely resistive load of \(50\Omega\) . The time taken for the current to rise from half of the peak value of the peak value is:
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\(2.2\,\,ms\)
\(3.3\,\,ms\)
\(5\,\,ms\)
\(7.2\,\,ms\)
The wavelength of the carrier waves in a modern optical fiber communication network is close to:
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\(1500\,nm\)
\(600\,nm\)
\(2400\,nm\)
\(900\,nm\)
Water from a pipe is coming at a rate of 100 litres per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of : (density of water = 1000 \(kg/m^3\) , coefficient of viscosity of water = 1 mPa s)
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\(10^3\)
\(10^6\)
\(10^2\)
\(10^4\)
A boy’s catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of cross – section and of negligible mass. The boy keeps a stone weighing 0.02 kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of 20 \(ms^{-1}\) . Neglect the change in the area of cross section of the cord while stretched. The Young’s modulus of rubber is closest to:
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\(10^3\,Nm^{-2}\)
\(10^6\,Nm^{-2}\)
\(10^8\,Nm^{-2}\)
\(10^4\,Nm^{-2}\)
Two particles move at right angle to each other. Their de Broglie wavelengths are \(\lambda_1\) and \(\lambda_2\) respectively. The particles suffere perfectly inelastic collision. The de Broglie wavelength \(\lambda\) , of the final particle, is given by:
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\(\lambda=\sqrt{\lambda_1\lambda_2}\)
\(\lambda=\frac{\lambda_1+\lambda_2}{2}\)
\(\frac{2}{\lambda}=\frac{1}{\lambda_1}+\frac{1}{\lambda_2}\)
\(\frac{1}{\lambda^2}=\frac{1}{\lambda_1^2}+\frac{1}{\lambda_2^2}\)
Four identical particles of mass M are located at the corners of a square of side ‘a’. What should be their speed if each of them revolves under the influence of other’s gravitational field in a circular orbit circumscribing the square?
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\(1.35\sqrt{\frac{GM}{a}}\)
\(1.16\sqrt{\frac{GM}{a}}\)
\(1.41\sqrt{\frac{GM}{a}}\)
\(1.21\sqrt{\frac{GM}{a}}\)
In figure, the optical fiber is \(l=2m\) long and has a diameter of \(d = 20\, \mu \,m\) . If a ray of light is incident on one end of the fiber at angle \(\theta_1=40^\circ\) , the number of reflection it makes before emerging from the other end is close to:
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\(57000 \)
\( 45000 \)
\( 66000\)
\(55000\)
Non of the above
A circular coil having N turns and radius r carries a current. It is held in the XZ plane in a magnetic field \(B\hat{i}\) . The torque on the coil due to the magnetic field is:
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\(\frac{Br^21}{\pi N}\)
zero
\(\frac{B\pi\,r^21}{ N}\)
\(B\pi\,r^2\,IN\)
Ship A is sailing towards north – east with velocity \(\vec{v}=30\hat{i}+50\hat{j}\) km/hr where \(\hat{i}\) points east and \(\hat{j}\) , north. Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards west at 10 km/hr. A will be at minimum distance from B ins:
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\(2.2 hrs. \)
\(4.2 hrs. \)
\( 2.6 hrs.\)
\(3.2 hrs. \)
A plane electromagnetic wave travels in free space along the x – direction. The electric field component of the wave at a particular point of space and time is \(E=Vm^{-1}\) along y – direction. Its corresponding magnetic filed component, B would be:
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\(2\times10^{-8}\) T along z – direction
\(6\times10^{-8}\, T\) along x – direction
\(6\times10^{-8}\)T along z- direction
\(2\times10^{-8}\) T along y – direction
A thermally insulted vessel contains 150 g of water at \(0^\circ\,C\) . Then the air from the vessel is pumped out a adiabatically. A fraction of water turns into ice and the rest evaporates at \(0^\circ\,C\) itself. The mass of evaporated water will be closes to:
(Latent heat of vaporization of water = \(2.10\times 10^6\,\,Jkg^{-1}\) and Laten heat of Fusion of water = \(3.36\times 10^5\,\,Jkg^{-1}\) )
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\(35 g\)
\( 150 g \)
\(130 g \)
\(20 g \)
Radiation coming from transition n = 2 to n = 1 of hydrogen atoms fall of \(He^+\)ions in n = 1 and n = 2 states. The possible. Transition of helium ions as they absorb energy from the radiation is:
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\(n=2\rightarrow n=4\)
\(n=2\rightarrow n=5\)
\(n=2\rightarrow n=3\)
\(n=1\rightarrow n=4\)
A \(200\,\Omega\) resistor has a certain color code. If one replaces the red color by green in the code, the new resistance will be:
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\(500\,\Omega\)
\(400\,\Omega\)
\(300\,\Omega\)
\(100\,\Omega\)
The reverse breakdown voltage of a Zener diode is 5.6 V in the given circuit .
The current \(I_z\) through the Zener is:
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\(10 \,mA \)
\(15 \,mA \)
\(7\, mA \)
\(17\, mA\)
A thin circular plate of mass M and radius R has its density varying as \(p(r)=p_{0}\) r with \(P_0\) as constant and r is the distance from its center. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is \(I=aMR^2\) . The value of the coefficient a is:
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\(\frac{8}{5}\)
\(\frac{1}{2}\)
\(\frac{3}{5}\)
\(\frac{3}{2}\)