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A copper and a tungsten plate having a thickness $\delta$ = 2mm each are riveted together so that at $0^{\circ }C$ they form a flat bimetallic plate. Find the average radius of the curvature of this plate at $t$ = ${200}^{\circ }C$. The coefficient of linear expansion for copper and tungsten are ${\alpha }_{Cu}$ = $1.7\times {10}^{-5}/K$ and ${\alpha }_W$ = $0.4\times {10}^{-5}/K$.

A block of mass $2\text{kg}$ is projected with a velocity $6\text{m/s}$ so that it climbs onto z smooth wedge of mass $1\text{kg}$. If the block does not leave the wedge, find the maximum height attained by the block. Take $g=10{\text{m/s}}^2$.

A particle $p$ is moving in a circle of radius '$a$' with a uniform speed $v$. $C$ is the centre of the circle and $AB$ is a diameter. When passing through $B$, the angular velocity of $p$ about $A$ and $C$ are in the ratio?

A very thin transparent film of soap solution of negligible thickness is seen under reflection of white light. Then the colour of the film appear to be :

A) blue

B) black

C) red

D) yellow

A ball is thrown vertically upwards with a velocity of 10 metre per second . Itreturns to the ground with a velocity of 9 metre per second . If g is 9.8 ,then the maximum height attained by the ball is nearly?

A man (mass$=70\text{kg}$) and his son (mass$=20\text{kg}$) are standing on a frictionless surface facing in same direction. The man pushes his son, so that he starts moving with a speed of $0.90{\text{ms}}^{-1}$ with respect to man. The speed of man with respect to the surface is

The force F is given in terms of time t and displacement x by the equation F = A cos Bx + C sin Dt. The dimensional formula of $\frac{D}{B}$ is

A vessel containing water is given a constant acceleration ‘a’ towards the right along a straight horizontal path. Which of the following diagrams in the figure represents the surface of the liquid?

A particle is moving along a circular path. The angular velocity, linear velocity, angular acceleration, and centripetal acceleration of the particle at any instant, respectively are $\overrightarrow{\omega },\overrightarrow{v},\overrightarrow{\alpha }$ and $\overrightarrow{a_c}$. Which of the following relations is not correct?

Two objects that are moving in the $xy$ plane on a frictionless floor collide head on. Assume that they form a closed isolated system. The following table gives the momentum components in $\text{kg m/s}$ before and after the collision. What are the missing values $(a,b)$ (in $\text{kg m/s}$)?
$$\begin{array}{ccccc}& \text{Before collision}& & \text{After collision}& \\ \text{Object}& P_x& P_y& P_x& P_y\\ A& -4& 5& 3& a\\ B& b& -2& 4& 2\end{array}$$

A pure resistance R, pure capacitance C and pure inductance L are connected in series and the impedance of the circuit at resonance is Z_o. If they are connected in parallel to each other, the maximum impedance at resonance will be:

Blocks A and C start from rest and move to the right with acceleration $a_A=12tm{s}^{-2}and{a}_C=3m{s}^{-2}$. Here t is in seconds. The time when block B again comes to rest is

A man pushes a immovable wall with a force F. Can the man ever push the wall with a force greater than his weight? The groudnon which the man is standing is rough.

A man is standing in a lift moving upwards with a constant speed of $10{\text{ms}}^{-1}$. The man drops a coin from a height of $4.9\text{m}$. If $g=9.8{\text{ms}}^{-2}$, the coin reaches the floor of the lift after a time

If 3${}^{16}$ x (2 m)${}^2$ = 6${}^{16}$ , then x is

Same spring is attached with 2kg, 3kg and 1 kg blocks in three different cases as shown in the figure. If $x_1,x_2\text{and}{x}_3$ be the extensions in the spring in these three cases then

A wire of length L and cross-sectional area A is made of a material of Young's modulus Y. The work one in stretching the wire by an amount x is given by

In problem 10.9, if 15.0 cm of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms? (Specific gravity of mercury = 13.6)

A spherical liquid drop is placed on a horizontal plane. A small disturbance causes the volume of the drop to oscillate. The time period of oscillation $\left(T\right)$ of the liquid drop depends on radius $\left(r\right)$ of the drop, density $\left(\rho \right)$ and surface tension $\left(S\right)$ of the liquid. Which among the following will be a possible expression for $T$ (where $k$ is a dimensionless constant)? (given surface tension is force per unit length)

If two points $P=(0,–1)$ and $Q=(4,1)$ are on a straight line, find equation of the Straight line.

As shown in figure from a uniform rectangular sheet a triangular sheet is removed from one edge. The shift of centre of mass is

If the earth stops rotating about its axis, then the magnitude of gravity

Which of the following correctly represents the truth table of the configuration of gates shown here?

The area between the curves y = x² and y = x³ is:

A small body of superdense material, whose mass is twice the mass of the earth but whose size is very small compared to the size of the earth, starts from rest at a height H<<R above the earth's surface, and reaches the earth's surface in time t. Then t is equal to

4g of metal oxide contains 1.6g oxygen, then equivalent mass of the metal is

What will be the derivative of a constant?

2 mole of zinc is dissolved in HCl at ${25}^{\circ }C$. The work done in open vessel is:

A simple pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limits -∅and +∅. For an angular displacement $\theta (|\theta |<\varphi )$ , the tension in the string and the velocity of the bob are T and v respectively. The following relations hold good under the above conditions

A train has a speed of 60 km/h for the first one hour and 40 km/h for the next half hour. Its average speed in km/h is

A block is lying on an inclined plane which makes ${60}^o$ with the horizontal. If coefficient of friction between block and plane is 0.25 and g=10 $m/s^2$, then acceleration of the block when it moves along the plane will be

Calculate the power developed when the force of 10 N is exerted on a body moving with velocity of 3.65 m/s.

In a children's park, there is a slide which has a total length of 10 m and a height of St m (figure 8-E3). Vertical ladder are provided to reach the top. A boy weighing 200 N climbs up the ladder to the top of the slide and slides down to the ground. The average friction offered by the slide is three tenth of his weight. (a) the work done by the boy on the ladder as he go: up, (b) the work done by the slide on the boy as he cornea down, (c) the work done by the ladder on the boy as he goes up. Neglect any work done by forces inside the body of the boy.

Trajectory of a projectile near the surface of Earth is $y=4x-12x^2$. If $y$ is vertical axis and $x$ is horizontal then angle of projection is

A Force $\overrightarrow{F}=-2k[y\hat{i}+x\hat{j}]N$ ,where $k$ is constant, acts on a particle moving in the $xy$ plane. Starting from the origin, the particle is taken along the positive $x-$axis to the point $(a,0)$ and then parallel to $y-$ axis to the point $(a,a)$. The total work done by the force $\overrightarrow{F}$ on the particle is

When a cylindrical tube is dipped vertically into a liquid, the angle of contact is ${140}^{\circ }$. When the tube is dipped with an inclination of ${40}^{\circ }$, then the angle of contact is: