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A block of mass $m$ is placed on the top of another block of mass $M$ as shown in the figure. The coefficient of friction between them is $\mu$. Maximum acceleration of $M$ such that $M$ and $m$ move together is (there is no friction between ground and $M$)

A beam of
light converges at a point P. Now a lens is placed in the path of the
convergent beam 12 cm from P. At what point does the beam converge if
the lens is (a) a convex lens of focal length 20 cm, and (b) a
concave lens of focal length 16 cm?

Light is incident on a glass plate $(\mu =1.5)$ such that angle of refraction is ${60}^{\circ }.$ Dark band is observed corresponding to the wave length of $6000\mathring{A}$. If the thickness of glass plate is $1.2\times {10}^{-3}\text{mm}.$ Calculate the order of the interference band for reflected system .

Two equal masses are attached to the two ends of a spring of spring constant $k$. The masses are pulled apart symmetrically to stretch the spring by a length $x$ over its natural length. The work done by the spring on each mass is:

A ball is thrown vertically upwards, it reaches the height $h$ and then returns to the initial position. Work done by gravity when ball moves upwards is $W_1$ and $W_2$ when ball moves in downward direction. Then

Particles of masses 1 g, 2 g, 3 g,...., 100 g are kept at the marks 1 cm, 2 cm, 3 cm, ....,100 cm respectively on a metre scale. Find the moment of inertia of the system of particles about a perpendicular bisector of the metre scale.

What will happen to the leaves of electroscope if positively charged body is brought near (a) uncharged electroscope (b) positively charged electroscope (c) negatively charged electroscope ?

Find the potential difference $V_a-V_b$ between points $a$ and $b$ as shown below.

The retarding acceleration of $4.9{\text{ms}}^{-2}$ due to frictional force stops the car of mass $400\text{kg}$ travelling on a road. The coefficient of friction between the tyre of the car and the road is

Write the function that relates the relation between x and y.

The average radius of a toroid, made out of a non-magnetic material, is $0.1\text{m}$ and it has $500$ turns. If it carries a $0.5\text{A}$ current, the intensity of magnetic field along its circular axis will be-

When a 12 V battery is connected across an unknown resistor, there is a current of 4 mA in the circuit. Find the value of the resistance of the resistor.

What is the capacitance between points $\text{A}$ and $\text{B}$ for the given assembly?

A point P lies on the axis of a flat coil carrying a current. The magnetic moment of the coil is $\pi$. The distance of P from the coil is d, which is large compared to the radius of the coil. The magnetic field at P has magnitude

The photo-electric cell is connected to a source of variable potential difference, connected across it and the resulting photo-electric current $\left(\mu A\right)$ is plotted against the applied potential difference (V). The graph in the broken line represents a case for a given frequency and intensity of the incident radiation. If the frequency is increased and the intensity is reduced, which of the following graphs of unbroken line represent the new situation?

Two blocks of masses M = 5 kg and m = 3 kg are placed on a horizontal surface as shown in the figure. The coefficient of friction between the blocks is 0.5 and that between the block M and the horizontal surface is 0.7. What is the maximum horizontal force F that can be applied to block M so that both the blocks move together?

The velocity of a particle moving along a line is $v=t^2-5t+6$, from $t=4$ to $t=8$. What is the relation between distance $\left(S\right)$ and displacement $\left(\Delta X\right)$

A particle moves along the sides AB, BC, and CD of a square of side 25 m with a speed of 15. Its average velocity is________.

Two ships are $80\text{km}$ apart on North-South vertical at an instant as shown in the figure. The one farther North is streaming South at $40\text{km/hr}$ and the other is streaming East at $30\text{km/hr}$. What is their distance of closest approach?

A small block of mass $m$ is placed over a long plank of mass $M$. Coefficient of friction between them is $\mu$. Ground is smooth. At $t=0$, $m$ is given a velocity $v_1$ and $M$ a velocity $v_2(>v_1)$ as shown in the figure. After this $M$ is maintained at constant acceleration $a(<\mu g)$.



Find the time $t_0$ when velocities of both block and plank become same.

A capacitor and resistor are connected with an $AC$ source as shown in the figure. Reactance of capacitor is $X_c=3\Omega$ and resistance of resistor is $4\Omega$. Phase difference between current $I$ and $I_1$ is $(\text{Take}{\tan }^{-1}\frac{4}{3}={53}^{\circ })$

A parachutist with total weight 75 kg drops vertically onto a sandy ground with a speed of 2 ms${}^{-1}$ and comes to a halt over a distance of 0.25m. The average force from the ground on her is close to.

A particle is moving three times as fast as an electron. The ratio of the de Broglie wavelength of the particle to that of the electron is $1.813\times {10}^{-4}.$ Calculate the particle’s mass. (Given mass of electron is $9.109\times {10}^{-31}kg)$

A block of mass m is pushed by applying a force F at an angle θ with the horizontal surface. The normal force on the block is given as -

A block of weight 100 N is lying on a rough horizontal surface .it's coefficient of friction is $\frac{1}{\sqrt{3}}$ the least possible force that can move the block is?

A square hole of side length $l$ is made at a depth of $h$ and a circular hole of radius $r$ is made at a depth of $4h$ from the surface of water in a water tank kept on a horizontal surface. If $l<<h$, $r<<h$ and the rate of water flow from the holes is the same, then $r$ is equal to -

Given a point source of light, which of the following can produce a parallel beam of light [CPMT 1974; KCET

Particle A moves uniformly with velocity v, so that vector v is continually aimed at point B which moves rectilinearly with a velocity u < v. At t = 0, v and u are perpendicular. Find the time when they converge. Assume A and B are separated by $l$ at t = 0.