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A small ball is projected along the surface of a smooth inclined plane with speed 10 m/s along the direction shown at t = 0. the point of projection is origin, z - axis is along vertical . The accelearation due to gravity is 10 m/ $s^2$. Lists values of certain parameters related to motion of ball and column - II linst fifferent time instants. Match appropriately.

"$$\begin{array}{cc}coloumn1& coloumn2\\ \left(p\right)Distancefromx-axis& \left(a\right)0.5\\ \left(q\right)Speedisminimum& \left(b\right)1.0\\ \left(r\right)Velocitymakesangel{37}^{\circ }withx-axis& \left(c\right)1.50\\ \left(s\right)Ballismaximumawayfromx-axis& \left(d\right)2.0\end{array}$$

A box is gently placed on a horizontal conveyer belt moving with a speed of $4m{s}^{-1}$. If the coefficient of friction between the box and the belt is 0.8, through what distance will the block slide without slipping? Take g = $10m{s}^{-2}$

Find the components of force F parallel and perpendicular to the incline surface.

Find the acceleration of the block of mass M in the situation of figure (6-E10). The coefficient of friction between the two blocks is ${\mu }_1$ and that between the bigger block and the ground is ${\mu }_2$.

Two condensers of capacities $2C$ and $C$ are joined in parallel and charged upto potential $V$. The battery is removed, and the condenser of capacity $C$ is filled completely with a medium of dielectric constant $K$. The potential difference across the capacitor will now be

If unit vectors $\hat{A}$ and $\hat{B}$ are inclined at an angle $\theta$, then $|\hat{A}-\hat{B}|$ is equal to

When a proton is released from rest in a room, it starts with an initial acceleration $a_0$ towards west. When it is projected towards north with a speed $v_0$ it moves with an initial acceleration $3a_0$ towards west. The electric and magnetic fields in the room are:

A wire of length $l$, mass $m$ and resistance $R$ slides without any friction, down the parallel conducting rails of negligible resistance (see figure). The rails are connected to each other at the bottom by a resistanceless rail parallel to the wire so that the wire and the rails form a closed rectangular conducting loop. The plane of the rails makes an angle $\theta$ with the horizontal and a uniform vertical magnetic field of induction B exists throughout the region. Find the steady state velocity of the wire.

Least count of a screw gauge is 0.001 cm. the diameter of a wire measuredby this instrument is 0.025 cm. the percentage error in the measurement is

A uniformly charged ring is partially inserted into a hypothetical spherical surface as shown. Find the flux through the sphere. They are both of the same radius as shown and both pass through each other's centres.

A free point charge q of mass m is at rest at the origin in a gravity free space. A constant electric field $E_0\hat{i}+E_0\hat{j}$ and a constant magnetic field $B_0(-\hat{k})$ is present in that region. The charge is set free to move. The speed of the charge when it reaches a position (2,2,0) is

A point object O is placed at a distance of $0.3\text{m}$ from a convex lens (focal length $0.2\text{m}$) cut into two halves each of which is displaced by $0.0005\text{m}$ as shown in the figure.



Find the spacing between the images so formed.

Differentiate between sky waves and ground waves.

A student is performing the experiment of resonance column. The diameter of the column tube is $6\text{cm}$. The frequency of the tuning fork is $504\text{Hz}$. The speed of the sound at the given temperature is $336\text{m/s}$. The zero of the meter scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is -

Which of the following is used in communication technology:

If the code of the fourth batch is ‘she when dirty get orange dust’, which of the following would be the code for the seventh batch?

Point masses of $1,2,3$ and $4\text{kg}$ are lying at the points $(0,0,0),(2,0,0),(0,3,0)\text{and}(-2,-2,0)$ respectively. What will be the moment of inertia of the system about $x$ - axis?

A simply supported beam of span L is subjected to a concentrated load W at midpsan. The strain energy due to bending in the beam would be

A body traveling along a straight line traversed first one third of the total distance with a velocity $3\text{m/s}$. The remaining part of the distance was covered with a velocity $2\text{m/s}$ for half the time and with velocity $6\text{m/s}$ for the other half of time. The mean velocity over the whole time of motion is

In which of the following, pressure exerted on the ground is the least?

For three capacitors of capacitance $2\mu \text{F}$, $4\mu \text{F}$, $8\mu \text{F}$ connected parallel to each other having applied voltages $20\text{V}$, $40\text{V}$, $60\text{V}$ respectively. Then the equivalent breakdown voltage of the combination is?

Two objects that are moving along an xy-plane on a frictionless floor collide. Assume that they form a closed, isolated system. The following table gives some of the momentum components (in kilogram meters per second) before and after the collision. What is the missing values (a, b):
$\begin{array}{ccc}& Beforecollision& Aftercollision\\ Object& P_x\mid P_y& P_x\mid P_y\\ A& -4\mid 5& 3\mid A\\ B& B\mid -2& 4\mid 2\end{array}$

A parallel plate capacitor of capacitance $90\text{pF}$ is connected to a battery of $20\text{V}$. If a dielectric material of dielectric constant $K=5/3$ is inserted between the plates, the magnitude of induced charge, will be

A ball of mass (m) 0.5 kg is attached to the end of a string having length (l) 0.5m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in rad/s) is

Maximum and minimum magnitudes of the resultant of two vectors of magnitude p and q are in the ratio 3:1. Which of the following options is correct?

Find the second order
derivatives of the function.