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A 20N metal block is suspended by a spring balance. A beaker containing some water is placed on a weighing machine which reads 40N. The spring balance is lowered such that that the block gets immersed in the water. The spring balance now reads 16N. The reading of the weighing machine will be

a)36N b)60N c)44N d)56N

If the force $\overrightarrow{F}=(60\hat{i}+15\hat{j}-3\hat{k})\text{N}$ and velocity $\overrightarrow{v}=(2\hat{i}-4\hat{j}+5\hat{k})\text{m/s}$, then instantaneous power is

Electron coming out from cathode is accelearated towards anode, if the gain in kinetic energy is $400\text{eV}$, what should be the distance between the two plates?

$[$Assume electric field between anode and cathod is $40\text{kN/C}]$.

A block of $10\text{kg}$ is pulled in a vertical plane along a frictionless surface in the form of an arc of a circle of radius $10\text{m}$. A force of $200\text{N}$ is applied such that tension in the string always remains along the tangential direction as shown in figure. If the block started from rest at $A$, the velocity at $B$ would be:

Consider $\frac{\pi }{3}=1$ for calculation and take $g=10{\text{m/s}}^2$)

A projectile is given an initial velocity of $(\hat{i}+2\hat{j})\text{m/s}.$ The cartesian equation of its path is $(g=10{\text{m/s}}^2)$

A swimmer crosses the river along the line making an angle of ${45}^{\circ }$ with the direction of flow. Velocity of the river water is $5\text{m/s}$. Swimmer takes 6 seconds to cross the river of width $60\text{m}$. The magnitude of velocity of the swimmer with respect to river will be

A charge of 1 $\text{coulomb}$ is placed at one end of a non-conducting rod of length $0.6\text{m}$. Half of the charge is removed from one end and placed on the other end. The rod is rotated in a vertical plane about a horizontal axis passing through the mid-point of the rod with angular frequency ${10}^4\pi \text{rad/s}$. The magnetic field at a point on the axis at a distance of $0.4\text{m}$ from centre of rod will be :

The velocity of the particle is given by $v=3t^2+2t$ in $\text{m/s}$. The acceleration and displacement of the particle as a function of time respectively are

[Take $x=0$ at $t=0$]

A
disc revolves with a speed of

rev/min, and
has a radius of 15 cm. Two coins are placed at 4 cm and 14 cm away
from the centre of the record. If the co-efficient of friction
between the coins and the record is 0.15, which of the coins will
revolve with the record?

The value of $\int \frac{\cos 5x}{\cos x}dx$ is

(where $C$ is constant of integration)

A man loses 20% of his velocity after running through $108\text{m}$. If his retardation is uniform, then the maximum total distance he can cover is

A rod of length l with resistance R lies in a constant uniform magnetic field $\overrightarrow{B}$ perpendicular to the rod. The surface is frictionless. The magnitude of the force that must be applied by a person to pull the rod at constant speed v is

A cubical wooden block of side L and relative density 0.5 is floating on the surface of water as shown in the figure. A string is attached by a pulley to it as shown. The graph of tension T in the string versus distance of the bottom of the block from the free surface of water when the end A of the rope is slowly being pulled up will be (block is moving)

Consider two concentric conducting spheres. The outer sphere is hollow and the inner sphere is solid. Initially, they are given a charge $-7Q$ and a charge $-2Q$ respectively, then the charges on the outer surface and inner surface of the outer sphere is

A concave lens doesn't have a focus because

Charges $-q$ and $+q$ located at $A$ and $B$ respectively, constitute an electric dipole. Distance $AB=2a$, $O$ is the mid point of the dipole and $OP$ is perpendicular to $AB$. A charge $Q$ is placed at $P$ where $OP=y$ and $y>>2a$. The charge $Q$ experiences an electrostatic force $F$. If $Q$ is now moved along the equatorial line to $P^{\prime }$ such that $O{P}^{\prime }=\left(\frac{y}{3}\right)$, the force on $Q$ will be close to

Here $(\frac{y}{3}>>2a)$

A stick of length L and mass M lies on a frictionless horizontal surface on which it is free to move in any way. A ball of mass m moving with speed v collides elastically with the stick as shown in figure. If after the collision, the ball comes to rest, then what should be the mass of the ball?

The plane wavefront shown in the diagram is travelling from air to water. $LM$ is the incident wavefront and $L^{\prime }{M}^{\prime }$ is the refracted wavefront. The wavefront $LM$ is obliquely incident on the surface of water at an angle of incidence ${60}^{\circ }$. If the distance $M{M}^{\prime }=10\text{cm}$, find distance $L{L}^{\prime }$. Take refractive index of water equal to $\frac{4}{3}$.

In the figure shown below, $u=\sqrt{7gl}$ and mass of the bob is $3\text{kg}$. Find the value of tension in the string when angle $\theta ={180}^{\circ }$ [Take $g=10{\text{m/s}}^2$]

A uniform chain of mass $m$ and length $l$ is lying on a frictionless horizontal table with one-third of its length hanging over the edge of the table. The amount of work done to pull the hanging part of the chain up to the table is given by

A body of mass $m={10}^{-2}$ kg is moving in a medium and experiences a frictional force F = $-k{v}^2$. Its initial speed is $v_0=10m{s}^{-1}$. If after 10 s, its energy is $\frac{1}{8}$ $m{v}_0^2$, the value of k will be

An ice cube of mass $M_0$ is given a velocity $v_0$ on a rough horizontal surface with coefficient of friction $\mu$. The block is at its melting point and latent heat of fusion of ice is $L$. The block receives heat only due to the friction forces and all work is converted into heat. Find the mass ($M_t$) of the remaining ice block after time $t$.

A magnet of mass $2\text{kg}$ is thrown with a velocity of $5\text{m/s}$ towards a moving metal block of unknown mass. Both magnet and block are moving along a smooth horizontal surface. After the collision, the magnet sticks to the metal block. If the initial momentum of system is $48\text{kg.m/s}$ and the initial velocity of $\text{COM}$ of system is $3\text{m/s}$, then what is the magnitude of initial velocity of the metal block?

What
is the area of the plates of a 2 F parallel plate capacitor, given
that the separation between the plates is 0.5 cm? [You will realize
from your answer why ordinary capacitors are in the range of µF
or less. However, electrolytic capacitors do have a much larger
capacitance (0.1 F) because of very minute separation between the
conductors.]

Let $F\left(x\right)=sinx{\int }_0^{x}costdt+2{\int }_0^{x}tdt+co{s}^{2}x-x^2$ . Then area bounded by xF(x) and ordinate x = 0 and x = 5 with x- axis is

The dimension of the stress is:

What is potential difference ?