JEE MAIN - Physics (2016 - 9th April Morning Slot)
- 1A 50 $$\Omega $$ resistance is connected to a battery of 5 V. A galvanometer of resistance 100 $$\Omega $$ is to be used as an ammeter to measure current through the resistance, for this a resistance rs is connected to the galvanometer. Which of the following connections should be employed if the measured current is within 1% of thecurrent without the ammeter in the circuit ?Odpověď(A)rs = 0.5 $$\Omega $$ in parallel with the galvanometer
- 3Figure shows elliptical path abcd of a planet around the sun S such that the area of triangle csa is $${1 \over 4}$$ the area of the ellipse. (See figure) With db as the semimajor axis, and ca as the semiminor axis. If t1 is the time taken for planet to go over path abc and t2 for path taken over cda then :
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Odpověď(C)t1 = 3t2 - 4To find the focal length of a convex mirror, a student records the following data :
Object
PinConvex
LensConvex
MirrorImage
Pin22.2 cm 32.2 cm 45.8 cm 71.2 cm
The focal length of the convex lens is f1 and that of mirror is f2. Then taking index correction to be negligibly small, f1 and f2 are close to :Odpověď(B)f1 = 7.8 cm f2 = 12.7 cm - 5A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2 s at T=0oC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is $$\alpha $$ then the value of S is :Odpověď(A)$$\alpha $$
- 6A uniformly tapering conical wire is made from a material of Young’s modulus Y and has a normal, unextended length L. The radii, at the upper and lower ends of this conical wire, have values R and 3 R, respectively. The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower end. The equilibrium extended length, of this wire, would equal :Odpověď(B)L $$\left( {1 + {1 \over 3}{{Mg} \over {\pi Y{R^2}}}} \right)$$
- 8In Young’s double slit experiment, the distance between slits and the screen is 1.0 m and monochromatic light of 600 nm is being used. A person standing near the slits is looking at the fringe pattern. When the separation between the slits is varied, the interference pattern disappears for a particular distance d0 between the slits. If the angular resolution of the eye is $$({{{1}} \over {60}})^o$$, the value of d0 is close to :Odpověď(B)2 mm
- 10When photons of wavelength $${\lambda _1}$$ are incident on an isolated sphere, the corresponding stopping potential is found to be V. When photons of wavelength $${\lambda _2}$$ are used, the corresponding stopping potential was thrice that of the above value. If light of wavelength $${\lambda _3}$$ is used then find the stopping potential for this case :Odpověď(C)$${{hc} \over e}\left[ {{1 \over {{\lambda _3}}} + {1 \over {2{\lambda _2}}} - {3 \over {2{\lambda _1}}}} \right]$$
- 12The potential (in volts) of a charge distribution is given by.
V(z) = 30 $$-$$ 5x2 for $$\left| z \right|$$ $$ \le $$ 1 m.
V(z) = 35 $$-$$ 10 $$\left| z \right|$$ for $$\left| z \right|$$ $$ \ge $$1 m.
V(z) does not depend on x and y. If this potential is generated by a constant charge per unit volume $${\rho _0}$$ (in units of $${\varepsilon _0}$$) which is spread over a certain region, then choose the correct statement.Odpověď(A)$${\rho _0}$$ = 10 $${\varepsilon _0}$$ for $$\left| z \right|$$ $$ \le $$ 1 m and $${\rho _0} = 0$$ elsewhere - 15Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to A and I, respectively. At time t = 0 one particle has displacement A while the other one has displacement $${{ - A} \over 2}$$ and they are moving towards each other. If they cross each other at time t, then t is :Odpověď(A)$${T \over 6}$$
- 19A car of weight W is on an inclined road that rises by 100 m over a distance of 1 km and applies a constant frictional force $${W \over 20}$$ on the car. While moving uphill on the road at a speed of 10 ms−1, the car needs power P. If it needs power $${p \over 2}$$ while moving downhill at speed v then value of $$\upsilon $$ is :Odpověď(B)15 ms$$-$$1
- 21A rocket is fired vertically from the earth with an acceleration of 2g, where g is the gravitational acceleration. On an inclined plane inside the rocket, making an angle $$\theta $$ with the horizontal, a point object of mass m is kept. The minimum coefficient of friction $$\mu $$min between the mass and the inclined surface such that the mass does not move is :Odpověď(A)tan$$\theta $$
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Consider a water jar of radius R that has water filled up to height H and is kept on astand of height h (see figure). Through a hole of radius r (r << R) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is x. Then :Odpověď(C)$$x = r{\left( {{H \over {H + h}}} \right)^{{1 \over 4}}}$$
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