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A projectile is fired with some velocity making certain angle with the horizontal. Which of the following graphs is the best representation for the kinetic energy of a projectile $\left(KE\right)$ versus its horizontal displacement $\left(x\right)$?

A rod of mass $m$ and length $2R$ is attached to a circular ring of mass $mandradiusR$ along its vertical diameter as shown. Horizontal force $F$ is applied at top. Friction is sufficient for pure rolling, then friction force acting on the ring, at the instant shown is

A block of mass $10\text{kg}$ is slowly slid up a smooth inclined plane of inclination ${37}^{\circ }$ by a person. Calculate the work done by the person in moving the block through a distance of $20\text{m}$ along the incline, if the person applies the force parallel to the inclined plane. Take $g=10{\text{m/s}}^2$.

A coil of radius 10 cm and resistance $40\Omega$ has 1000 turns. It is placed with its plane vertical and its axis parallel to the magnetic meridian. The coil is connected to a galvanome ter and is rotated about the vertical diameter through an angle of ${180}^{\circ }.$ Find the charge which flows through the galvanometer if the horizontal component of the earth's magnetic field is $B_H=3.0\times {10}^{-5}T.$

1. 540

If Rohit moves along a circular path from point $A(0,0)$ as shown in the figure and reaches diametrically opposite point $B(5,0)$, what is his displacement vector? Given: radius of circle is $2.5$ unit.

A cylinder fixed with a piston contains saturated vapour of a refrigerant at ${10}^{\circ }C,$ the volume and pressure are $10\text{L}$ and $0.681\text{MPa}$ respectively. The refrigerant is compressed to $3.5\text{L}$ and $2\text{MPa}$. If the saturated vapour is undergoing polytropic process as $P{V}^n=$ constant, where $n=1.025,$ then calculate the work done during the process.

A mixture of $4\text{g}$ of hydrogen and $8\text{g}$ of helium at NTP has a density about

A wire in the form of a circular loop of radius r lies with its plane normal to a magnetic field B. If the wire is polled to take a square shape in the same plane in time t, the emf induced in the loop is given by

The point $A$ moves with a uniform speed along the circumference of a circle of radius $0.36\text{m}$ and cover ${30}^{\circ }$ in $0.1\text{s}$. The perpendicular projection ${}^{\prime }{P}^{\prime }$ from ${}^{\prime }{A}^{\prime }$ on the diameter $MN$ represents the simple harmonic motion of ${}^{\prime }{P}^{\prime }$. The restoring force per unit mass when $P$ touches $M$ will be:

Electric potential in a region is varying according to the relation $V=\frac{3x^2}{2}-\frac{y^2}{4}$ , where $x$ and $y$ are in $\text{meter}$ and $V$ is in $\text{volt}$. Electric field intensity in $\text{N/C}$ at a point $(1\text{m},2\text{m})$ is

Metallic spheres of radius 1 cm and 2 cm are given charges 10^-2 and5*10^-2, respectively if they are connected by a conducting wire the final charge on the smallest Sphere is

Find the velocity of water in pipe for the arrangement of pitot-tube shown

A uniform chain of mass M and length L is held vertically in such a way that its lower end just touches the horizontal floor. The chain is released from rest in this position. Any portion that strikes the floor comes to rest. Assuming that the chain does not form a heap on the floor, calculate the force exerted by it on the floor when a length x has reached the floor.

In a $\Delta ABC,$ let $2a^2+4b^2+c^2=2a(2b+c),$ then which of the following is/are true:

A machine gun fires a steady stream of bullets at the rate of $n$ per minute into a stationary target in which the bullets get embedded. If each bullet has a mass $m$ and arrives at the target with a velocity $v$, the average force on the target is

A system of three polarizers $P_1,P_2,P_3$ is set up such that the pass axis of $P_3$ is crossed with respect to that of $P_1$. The pass axis of $P_2$ is inclined at ${60}^{\circ }$ to the pass axis of $P_3.$ When a beam of unpolarized light of intensity $I_0$ is incident on $P_1$, the intensity of light emerging from $P_3$ is $I$. The ratio $\left(I_0/I\right)$ equals (nearly),

A ray is incident at a small angle of incidence $i$ on one face of a prism with angle of prism $6^{\circ }$ and emerges from the second face. If the prism is dipped in transparent liquid of refractive index $1.2$ and angle of deviation is $2^{\circ }$, then what is the refractive index of prism material?

Find the average angular speed of the minute hand of a normal clock in $1.5\text{hrs}$.

1. 300

Find the angle by which the mirror must be rotated such that the reflected ray will be travelling along the vertical (dotted line) as shown in the figure.

[CW - clockwise, CCW - counter-clockwise]

A parallel plate capacitor is made of square plates, each of length $l$ separated by a distance $t$ as shown. Capacity when the plates are making small angle $\theta$ with each other as shown in the diagram is $C$, if the square plates are of length $2l$ and separated by distance $2t$ and make the same angle $\theta$, then capacity is $C^{\prime }$ which of the following correctly represent the relation between $C$ and $C^{\prime }$