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Two rods, $A$ and $B$, of different materials having the same cross-sectional area are welded together as shown in the figure. Their thermal conductivities are $K_1$ and $K_2$. The thermal conductivity of the composite rod will be:
A block of mass $M=5 \text{ kg}$ is resting on a rough horizontal surface for which the coefficient of friction is 0.2. When a force $F=40 \text{ N}$ is applied, the acceleration of the block will be: ($g=10 \text{ m/s}^2$)
A particle of mass $m$ moves in the $XY$ plane with a velocity of $v$ along the straight line $AB$. If the angular momentum of the particle about the origin $O$ is $L_A$ when it is at $A$ and $L_B$ when it is at $B$, then:
A lens of large focal length and large aperture is best suited as an objective of an astronomical telescope since
The ratio of the accelerations for a solid sphere (mass $m$ and radius $R$) rolling down an incline of angle $\theta$ without slipping and slipping down the incline without rolling is:
Three blocks of masses $m_1$, $m_2$ and $m_3$ are connected by massless strings as shown on a frictionless table. They are pulled with a force $T_3 = 40 \text{ N}$. If $m_1 = 10 \text{ kg}$, $m_2 = 6 \text{ kg}$ and $m_3 = 4 \text{ kg}$, the tension $T_2$ will be:
A light and a heavy body have equal momenta. Which one has greater K.E.?
A body cools from a temperature $3T$ to $2T$ in $10\text{ minutes}$. The room temperature is $T$. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next $10\text{ minutes}$ will be:
Two persons of mass $55 \text{ kg}$ and $65 \text{ kg}$ respectively, are at the opposite ends of a boat. The length of the boat is $3.0 \text{ m}$ and weighs $100 \text{ kg}$. The $55 \text{ kg}$ man walks up to the $65 \text{ kg}$ man and sits with him. If the boat is in still water the centre of mass of the system shifts by:
A spherical black body with a radius of $12\text{ cm}$ radiates $450\text{ W}$ power at $500\text{ K}$. If the radius were halved and the temperature doubled, the power radiated in watts would be:
A man of mass 80 kg is standing in an elevator which is moving with an acceleration of 6 m/s² in the upward direction. The apparent weight of the man will be (g = 10 m/s²):
DNA fingerprinting involves identifying differences in some specific regions in DNA sequence, called as
The quantities of heat required to raise the temperature of two solid copper spheres of radii $r_1$ and $r_2$ ($r_1=1.5 r_2$) through $1\text{ K}$ are in the ratio:
A ball of mass 0.5 kg moving with a velocity of 2 m/s strikes a wall normally and bounces back with the same speed. If the time of contact between the ball and the wall is one millisecond, the average force exerted by the wall on the ball is:
A uniform rod of length $200 \text{ cm}$ and mass $500 \text{ g}$ is balanced on a wedge placed at $40 \text{ cm}$ mark. A mass of $2 \text{ kg}$ is suspended from the rod at $20 \text{ cm}$ and another unknown mass $m$ is suspended from the rod at $160 \text{ cm}$ mark as shown in the figure. What would be the value of $m$ such that the rod is in equilibrium? (Take $g=10 \text{ m/s}^2$)
A piece of iron is heated in a flame. It first becomes dull red then becomes reddish yellow and finally turns to white hot. The correct explanation for the above observation is possible by using
A 500 kg car takes a round turn of radius 50 m with a velocity of 36 km/hr. The centripetal force is:
When a uranium isotope $^{235}_{92}\text{U}$ is bombarded with a neutron, it generates $^{89}_{36}\text{Kr}$, three neutrons and :
In an elevator moving vertically up with an acceleration $g$, the force exerted on the floor by a passenger of mass $M$ is:
A body of mass 5 kg is moving in a circle of radius 1 m with an angular velocity of 2 rad/s. The centripetal force is: