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Find the torque about the origin when a force of $3\hat{j} \text{ N}$ acts on a particle whose position vector is $2\hat{k} \text{ m}$.
If the acceleration due to gravity at a height 1 km above the earth is similar to a depth d below the surface of the earth, then:
A round disc of moment of inertia $I_2$ about its axis perpendicular to its plane and passing through its center is placed over another disc of moment of inertia $I_1$ rotating with an angular velocity $\omega$ about the same axis. The final angular velocity of the combination of discs is:
The force-time (F – t) curve of a particle executing linear motion is as shown in the figure. The momentum acquired by the particle in the time interval from zero to 8 seconds will be:
The average kinetic energy of a gas molecule can be determined by knowing:
The kinetic energy of one gram molecule of a gas at standard temperature and pressure is: (R = 8.31 J/mol-K)
A heavy uniform chain lies on a horizontal table-top. If the coefficient of friction between the chain and table surface is 0.25, then the maximum fraction of the length of the chain that can hang over one edge of the table is:
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):
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: