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A cylindrical drum, pushed along by a board rolls forward on the ground. There is on slipping at any contact. Find the distance moved by the man who is pushing the board, when axis of the cylinder covers a distance L.

A ring is rolling on a horizontal surface without slipping. Find the ratio of translation K.E. to rotational K.E. of ring.

A body falls from a height 'h' on a horizontal surface and rebounds. Then it falls again and again rebounds and so on. If the restitution coefficient is $\frac{1}{3}$, the total time taken by the body to come to rest is

Electric field in space is given as $\overrightarrow{E}=-2x^2\hat{i}+y\hat{j}-2z\hat{k}$. If potential of point $P(3,2,0)$ is $8$ volt, then potential at origin is:

Two uniform identical rods each of mass $M$ and length $l$ are joined to form a cross as shown in figure. Find the moment of inertia of the cross about a bisector as shown dotted in the figure.

A moth is at a distance of $10cm$ in front of a plane mirror. An observer is standing at a distance of $30cm$ in front of the mirror. Calculate the distance between the observer and the position of the moth's image.

A car travelling on a level road with a curve of radius $32\text{m}$. The coefficient of static friction between the road and tyre of car is $0.2$. What speed will put the car on verge of sliding? $(g=10{\text{m/s}}^2)$

A uniform but time varying magnetic field B(t) exists in a circular region of radius a and is directed into the plane of the paper as shown in Fig. 25.21.

The magnitude of the induced electric field at point P at a distance r from the centre of the circular region

A small block oscillates back and forth on a smooth concave surface of radius R. The time period of small oscillation is

Mean value of a.c. over half a cycle is

A force $F=0.5x+10$ acts on a particle in the x direction. Here $F$ is in newton and $x$ is in metre. Calculate the work done by the force during the displacement of the particle from $x=0$ to $x=2$ metre.

A body is projected with an initial velocity of $20\hat{i}+20\hat{j}$. It clears a wall at a distance of 20 m. Find the velocity when it clears the wall.

A particle of mass m is attached to three identical springs A, B and C each of force constant k as shown in figure. If the particle of mass m is pushed slightly against the spring A and released, the time period of oscillation is:

A block is resting on a piston which is moving vertically with SHM of period 1 s. What is the minimum amplitude to be given to it so that the block and piston can separate?

Two identical uniform rods $\text{EF}$ and $\text{GH}$, each of length $L=6\text{cm}$ are joined as shown in figure. Locate the centre of mass of the frame.
[Point $\text{O}$, which is the point where the axes of the rods meet is the origin]

What is the moment of inertia of a solid sphere about its diameter?

Two blocks of masses $m_1=4kg$ and $m_2=6kg$ are connected by a string of negligible mass passing over a frictionless pulley as shown in the figure. The coefficient of friction between block $m_1$ and the horizontal surface is 0.4. When the system is released, the masses $m_{1}and{m}_2$ start accelerating. What additional mass $m$ should be placed over mass $m_1$ so that the masses $(m_1+m)$ slide with a uniform speed?

The current in a long solenoid of radius R and having n turns per unit length is given $i=i_0\sin \omega t.$ A coil having N turns is wound around it near the centre. Find (a) the induced emf in the coil and (b) the mutual inductance between the solenoid and the coil.

The magnetic field at a point, 10 cm away from a magnetic dipole, is found to be 2.0 $\times {10}^{-4}$T. Find the magnetic moment of the dipole if the point is (a) in end -on position of the dipole and (b) in broadside-on position of the dipole.

A source of sound S and a detector D are placed at some distance from one another. A big cardboard is placed near the detector and perpendicular to the line SD as shown in figure (16-E1). It is gradually moved away and it is found that the intensity changes from a maximum to a minimum as the board is moved through a distance of 20 cm. Find the frequency of the sound emitted. Velocity of sound in air is 336 m/s.

If x is the distance of an object from the focus of a concave mirror and y is the distance of image from the focus, then which of the following graphs is correct between x and y

In Young's double slit experiment $62$ fringes are visible in the field of view with sodium light $(\lambda =5893\AA )$. If green light $(\lambda =5461\AA )$ is used then the number of visible fringes will be

Two particles are projected simultaneously from two points, O and O' such that d is the horizontal distance and h is the vertical distance between them. They are projected at the same inclination a to the horizontal with the same speed v. The time after which their separation becomes minimum is

If an antenna radiating electromagnetic waves has a height of 500 m, the range covered by it is (take R radius of earth as 6400 km)

When a galvanometer is shunted with a 4Ω resistance, the deflection is reduced to one-fifth. If the galvanometer is further shunted with a a 2Ω wire, determine current in galvanometer now if initially current in galvanometer is I₀ (given main current remains same).

A cubical block of wood of edge 3 cm floats in water. The lower surface of the cube just touches the free end of a vertical spring fixed at the bottom of the pot. Find the maximum weight that can be put on the block without wetting the new weight. Density of wood $=800{\text{kg/m}}^3$ and spring constant of the spring $=50\text{N/m}.(\text{Take g}=10{\text{m/s}}^2)$

On Earth a spring stretches by 4 cm when 100 gram is hung from it, now this spring is taken to moon and 250 gram mass is attached to spring, calculate time period of motion

Three blocks $m_1,m_2$ and $m_3$ of masses $8\text{kg},3\text{kg}$ and $1\text{kg}$ are placed in contact on a smooth surface. Forces $F_1=140\text{N}$ and $F_2=20\text{N}$ are acting on blocks $m_1$ and $m_3$ respectively as shown. The reaction between blocks $m_2$ and $m_3$ is

Calculate the velocity of the image with respect to a stationary observer in the following situation (Object moving at an angle with mirror and mirror moving at an angle with object).

A boy walks to his school at a distance of $9km$ with constant speed of $3km{h}^{-1}$ and walks back with a constant speed of $6km{h}^{-1}$. His average speed for round trip in ($km{h}^{-1}$) is

A particle executes simple harmonic oscillation. Its amplitude is $a$. The period of oscillation is $T$. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is

In the equation $x=A\sin (\omega t+\frac{\pi }{4})$. Match the following, when $x=\frac{A}{2}$

$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{(A) Kinetic energy}& \text{(p) Half the maximum value}\\ \text{(B) Potential energy}& \text{(q) 3/4 times the maximum value}\\ \text{(C) Acceleration}& \text{(r) 1/4 times the maximum value}\\ & \text{(s) Cannot say anything}\end{array}$

In the circuit shown below, what will be the readings of the voltmeter and ammeter

The refracting angle of a prism is A, and refractive index of the material of the prism is cot $\left(\frac{A}{2}\right)$. The angle of minimum deviation is :

The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the Centre is 54 $\mu T$. What will be its value at the centre of loop?

In a snooker game, a player strikes the white ball and imparts a velocity of $4\text{m/s}$. The white ball strikes another red ball which was initially at rest. Assuming that the collision of the balls is perfectly elastic and masses of both balls are the same, what are the velocities of the red and white balls respectively?

A $20\text{kg}$ monkey slides down a vertical rope with a constant acceleration of $7{\text{m/s}}^2$. If $g=10{\text{m/s}}^2$, what is the tension in the rope ?

A big drop of radius $R$ is formed by 729 small drops of water of radius $r$, then the radius of each small drop will be :

Two rods $PQ$ and $RS$ of identical mass and lengths $12\text{cm}$ and $18\text{cm}$ are joined to form a $T$ - shaped frame as shown in the figure. If the centre of mass of a rod is at the mid point of the rod, the location of centre of mass of the $T$ - shaped frame (w.r.t point $R$) is