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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 light and a heavy body have equal momenta. Which one has greater K.E.?
A rod of weight $w$ is supported by two parallel knife edges A and B and is in equilibrium in a horizontal position. The knives are at a distance $d$ from each other. The centre of mass of the rod is at distance $x$ from A. The normal reaction on A is:
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 bodies of mass $4 \text{ kg}$ and $6 \text{ kg}$ are tied to the ends of a massless string. The string passes over a pulley, which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity ($g$) is:
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?
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 average force necessary to stop a bullet of mass 20 g moving with a speed of 250 m/s, as it penetrates into the wood for a distance of 12 cm is:
DNA fingerprinting involves identifying differences in some specific regions in DNA sequence, called as
Two objects of mass $10 \text{ kg}$ and $20 \text{ kg}$ respectively are connected to the two ends of a rigid rod of length $10 \text{ m}$ with negligible mass. The distance of the center of mass of the system from the $10 \text{ kg}$ mass is:
A particle having a mass of $10^{-2}$ kg carries a charge of $5 \times 10^{-8}$ C. The particle is given an initial horizontal velocity of $10^5$ ms$^{-1}$ in the presence of electric field $\vec{E}$ and magnetic field $\vec{B}$. To keep the particle moving in a horizontal direction, it is necessary that: (1) $\vec{B}$ should be perpendicular to the direction of velocity and $\vec{E}$ should be along the direction of velocity. (2) Both $\vec{B}$ and $\vec{E}$ should be along the direction of velocity. (3) Both $\vec{B}$ and $\vec{E}$ are mutually perpendicular and perpendicular to the direction of velocity. (4) $\vec{B}$ should be along the direction of velocity and $\vec{E}$ should be perpendicular to the direction of velocity. Which one of the following pairs of statements are possible?