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A uniform solid cylinder of density 0.8g/cm^3 floats in equilibrium in a combination of two non-mixing liquids A and B with its axis vertical. The densities of the liquids A and B are 0.7g/cm^3 and 1.2g/cm^3, respectively. The height of liquid A is hA=1.2cm. The length of the part of the cylinder immersed in liquid B is hB=0.8cm. (a) Find the total force exerted by liquid A on the cylinder. (b) Find h, the length of the part of the cylinder in air. (c) The cylinder is depressed in such a way that its top surface is just below the upper surface of liquid A and is then released. Find the acceleration of the cylinder immediately after it is released.
28
Aug
A uniform solid cylinder of density 0.8g/cm^3 floats in equilibrium in a combination of two non-mixing liquids A and B with its axis vertical. The densities of the liquids A and B are 0.7g/cm^3 and 1.2g/cm^3, respectively. The height of liquid A is hA=1.2cm. The length of the part of the cylinder immersed in liquid [...]
A man is coming down an incline of angle 30 degree . When he walks with speed 2 sqrt3 m/s he has to keep his umbrella vertical to protect hismself from rain. The actual speed of rain is 5m/s . At what angle with vertical should he keep his umbrella when he is at rest so that he does not get drenched ?
28
Aug
A man is coming down an incline of angle 30 degree . When he walks with speed 2 sqrt3 m/s he has to keep his umbrella vertical to protect hismself from rain. The actual speed of rain is 5m/s . At what angle with vertical should he keep his umbrella when he is at rest [...]
A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2 m/s. When the stone reaches the floor,the distance of the man above the floor will be
28
Aug
A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2 m/s. When the stone reaches the floor,the distance of the man above the floor will be A man of 50 [...]
A container of large uniform cross-sectional area A resting on a horizontal surface, holds, two immiscible, non-viscous and incompressible liquids of densities d and 2d each of height H/2 as shown in the figure. The lower density liquid is open to the atmosphere having pressure P 0 .A homogeneous solid cylinder of length L(L<H/2), cross-sectional area A/5 is immersed such that it floats with its axis vertical at the liquid-liquid interface with length L/4 in the denser liquid. The cylinder is then removed and the original arrangement is restored. A tiny hole of area s(s<<A) is punched on the vertical side of the container at a height h(h<H/2). As a result of this, liquid starts flowing out of the hole with a range x on the horizontal surface. The horizontal distance traveled by the liquid, initially, is :
28
Aug
A container of large uniform cross-sectional area A resting on a horizontal surface, holds, two immiscible, non-viscous and incompressible liquids of densities d and 2d each of height H/2 as shown in the figure. The lower density liquid is open to the atmosphere having pressure P 0 .A homogeneous solid cylinder of length L(L<H/2), [...]
Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are v and 2v at any instant, then the speed of centre of mass of the system will be
28
Aug
Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are v and 2v at any instant, then the speed of centre of mass of the system will be move towards each other under the action of their internal attraction. If their speeds are [...]
A person standing on a road has to hold his umbrella at 60 degree with the vertical to keep the rain away. he throws the umbrella and starts running at a speed of 20 m/s. He finds that the rain drops are hitting his head vertically. Find the speed of rain drops with respect to A. the road B. the moving person
28
Aug
A person standing on a road has to hold his umbrella at 60 degree with the vertical to keep the rain away. he throws the umbrella and starts running at a speed of 20 m/s. He finds that the rain drops are hitting his head vertically. Find the speed of rain drops with respect to [...]
Two persons of masses 55 kg and 65 kg respectively, are at the opposite ends of the boat. The length of the boat is 3.0 m and weigh 100 kg. The 55 kg man walks to the 65 kg man and sits with him. If the boat is in stil water the centre of mass of the system shifts by
28
Aug
Two persons of masses 55 kg and 65 kg respectively, are at the opposite ends of the boat. The length of the boat is 3.0 m and weigh 100 kg. The 55 kg man walks to the 65 kg man and sits with him. If the boat is in stil water the centre of mass [...]
A container of large uniform cross sectional area A resting on a horizontal surface holds two immiscible non-viscous and incompressible liquids of density d and 3d each of height H/2. The lower density liquid is open to the atmosphere having pressure Po. A tiny hole of area a (a<<A) is punched on the vertical side of the lower container at a height h(0<h<H/2) for which range is maximum.
28
Aug
A container of large uniform cross sectional area A resting on a horizontal surface holds two immiscible non-viscous and incompressible liquids of density d and 3d each of height H/2. The lower density liquid is open to the atmosphere having pressure Po. A tiny hole of area a (a<<A) is punched on the vertical side [...]
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2 and 3 in the limbs in steady state ,
A cylindrical tank having cross-sectional area `A = 0.5 m^(2)` is filled with two liquids of density `rho_(1)=900 kg m^(-3)` and `rho_(2)=600 kgm^(-3)` ,
A vertical U-tube has a liquid up to a height h. If the tube is slowly rotated to an angular speed ω=g/h−−√ find the (i) heights of the liquid column ,
ii pressures at the points 1 ,
Two bodies of masres 1 kg and 3 kg have position vectors i^ + 2j^ + k^ and − 3i − 2j^ + k^ respectively. The centre of mass of this system has a position vector
28
Aug
Two bodies of masres 1 kg and 3 kg have position vectors i^ + 2j^ + k^ and − 3i − 2j^ + k^ respectively. The centre of mass of this system has a position vector Two bodies of masres 1kg and 3kg have position vectors i^+2j^ + k^ and − 3i − 2j^ + [...]
A standing man observes rain falling with the velocity of 20 m/ s^-1 at an angle of 30 degree with the vertical. (a) Find the velocity with which the amn should move so that rain appears to fall vertically to him. Now if he further increases his speed, rain again appears to fall at 30 degrees with the vertical. Find his new velocity.
28
Aug
A standing man observes rain falling with the velocity of 20 m/ s^-1 at an angle of 30 degree with the vertical. (a) Find the velocity with which the amn should move so that rain appears to fall vertically to him. Now if he further increases his speed, rain again appears to fall at 30 [...]