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JEE Physics Solved Question Paper 2015

Multiple Choice Questions

1.
A particle is projected with a velocity v so that its horizontal range twice the greatest height attained. The horizontal range is

$\frac{4 v^{2}}{5 g}$

$\frac{v^{2}}{g}$

$\frac{v^{2}}{2 g}$

$\frac{2 v^{2}}{3 g}$

$\frac{4 v^{2}}{5 g}$

Given, a particle having honzontal range is twice the greatest height attained by it, i.e,

$R = 2 H \frac{v^{2} \sin 2 θ}{g} = \frac{2 v^{2} \sin^{2} θ}{2 g} \Rightarrow 2 \sin θ \cos θ = \sin^{2} θ \Rightarrow \tan θ = 2 \Rightarrow \sin θ = \frac{2}{\sqrt{5}}, \cos θ = \frac{1}{\sqrt{5}}$

$Horizontal range, R = \frac{v^{2} \sin 2 θ}{g} = \frac{v^{2} \times 2 \sin θ \cos θ}{g} R = v^{2} \times \frac{2}{\sqrt{g}} \times \frac{2}{\sqrt{5}} \times \frac{1}{\sqrt{5}} R = \frac{4 v^{2}}{5 g}$

The velocity-time graph for two bodies A and B are shown in figure. Then, the acceleration of Aand B are in the ratio

sin 25° to sin 50°
tan 25° to tan 40°
cos 25° to cos 50°
tan 25° to tan 50°

The ratio of the dimensions of Planck's constant and that of moment of inertia has the dimensions of

angular momentum
time
velocity
frequency

Moment of inertia of a thin uniform rod rotating about the perpendicular axis passing through its centre is I. Ifthe same rod is bent into a ring and its moment of inertia about its diameter is I', then the ratio $\frac{I}{I'}$ is

$\frac{2}{3} π^{2}$
$\frac{3}{2} π^{2}$
$\frac{5}{3} π^{2}$
$\frac{8}{3} π^{2}$

If the mass of a body is M on the surface of the Earth, the mass of the same body on the surface of the Moon is

6 M
$\frac{M}{6}$
zero
M

The ratio of angular speed of a second-hand to the hour- hand of a watch is

$\frac{3600}{1}$
$\frac{720}{1}$
$\frac{72}{1}$
$\frac{60}{1}$

The kinetic energy of a body ofmass 4 kg and momentum 6 N-s will be

4.5 J
2.5 J
5.5 J
3.5 J

A stone of mass 0.05 kg is thrown vertically upwards. What is the direction and magnitude of net force on the stone during its upward motion ?

0.98 N vertically downwards
0.49 N vertically downwards
9.8 N vertically downwards
0.49 N vertically upwards

The ratio of kinetic energy to the potential energy of a particle executing SHM at a distance equal to half its amplitude, the distance being measured from its equilibrium position is

2 : 1
3 : 1
8 : 1
4 : 1