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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:
From a circular ring of mass $M$ and radius $R$, an arc corresponding to a $90^\circ$ sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is $K$ times $MR^2$. The value of $K$ will be:
The kinetic energy of one gram molecule of a gas at standard temperature and pressure is: (R = 8.31 J/mol-K)
When two surfaces are coated with a lubricant, then they:
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:
A piece of ice falls from a height $h$ so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice. The value of $h$ is: [Latent heat of ice is $3.4 \times 10^5 \text{ J/kg}$ and $g = 10 \text{ N/kg}$]
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:
Consider a car moving along a straight horizontal road with a speed of 72 km/h. If the coefficient of kinetic friction between the tyres and the road is 0.5, the shortest distance in which the car can be stopped is (g = 10 m/s²):
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: ($g=10 \text{ m/s}^2$)
The power radiated by a black body is $P$ and it radiates maximum energy at wavelength $\lambda_0$. Temperature of the black body is now changed so that it radiates maximum energy at the wavelength $\frac{3}{4}\lambda_0$. The power radiated by it now becomes $nP$. The value of $n$ is:
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
It is easier to draw up a wooden block along a smooth inclined plane than to haul it vertically, principally because:
A lift of mass $1000 \text{ kg}$ is moving with an acceleration of $1 \text{ m/s}^2$ in the upward direction. Tension developed in the string, which is connected to the lift, is:
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:
A major breakthrough in the studies of cells came with the development of an electron microscope. This is because:
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 monkey of mass $20 \text{ kg}$ is holding a vertical rope. The rope will not break when a mass of $25 \text{ kg}$ is suspended from it but will break if the mass exceeds $25 \text{ kg}$. What is the maximum acceleration with which the monkey can climb up along the rope ($g = 10 \text{ m/s}^2$)?
A force vector applied on a mass is represented as $\vec{F} = 6\hat{i} - 8\hat{j} + 10\hat{k}$ and accelerates with $1 \text{ m/s}^2$. What will be the mass of the body?