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It is option D
Any vector can be expressed as a sum of 3 perpendicular unit vectors, each multiplied by some number(the component of vector along that axis)
In the picture attached, the vector a has 3 different components along 3 perpendicular axes x,y,z and these components need not be equal all the times
Only false statement is : Option (C)
In the image attached it is clear that distance(total path length) is greater than displacement. Rest of the options are true.
For a freely falling body, there no other forces acting on the body other than gravity. (If you assume that there is no air resistance). The gravity force is nothing but the weight of the body which is constant. Since Force = mass * acceleration and mass is constant, so acceleration due to gravity is constant which is 9.81 m/s^2
Displacement, Velocity and speed increases as it falls but acceleration due to gravity is constant for earth
Option C
Vector addition is the right way to add any number of vectors
In vector addition, we add the magnitudes of each unit vector separately
The same applies for the subtraction also which is shown in figure
Assumptions : No effect of air, gravity change due to height
Force = mg = 0.002*10 = 0.02 N (since 2 g = 0.002 kg)
Displacement = height = 1km = 1000 m
Work done = Force * displacement
Work done = 0.02*1000 = 20 N.m
Note : in the question the velocity which is mentioned is 50 m/s but since it is given in the question that g value is 10m/s^2 which is constant , the velocity should be = sqrt(2gh) = sqrt(2*10*1000) = 141.4 m/s
Option B
Linear momentum = mass*velocity and all the velocities are vector quantities,
so linear momentum is also a vector (since mass is scalar)
But for current flowing in a wire we mention just a number (like 2 Amperes) but not the direction
Assumptions : No effect of air, gravity change due to height
Force = mg = 0.002*10 = 0.02 N (since 2 g = 0.002 kg)
Displacement = height = 1km = 1000 m
Work done = Force * displacement
Work done = 0.02*1000 = 20 N.m
Potential energy of bob is converted to kinetic energy and the energy lost during transition is 5%
Total energy intially = mgh
Total energy final = 0.5*mv^2
Energy lost = 5% of mgh = 0.05*mgh
So intial energy = final energy + loss
Given flow rate = 30 m^3 in 15 min = 2 m^3/min = 1/30 m^3/s
mass flow rate = vol. flow rate*density = 1/30 * 1000 = 100/3 kg/s
Power required = (mass flow rate)*g*h = 100/3*10*40 = 40000/3 Watts = 40/3 kW
But since efficiency is 30% - (if 100 W is consumed only 30 W will be supplied)
Total power consumed = power required/efficiency = (40/3)/0.3 = 44.44 kW
Answer : 2m/s
The formulas for velocities after collision is mentioned in the picture
Thumbrule : If 2 equal masses collide with each other with v1, v2 velocities then their final velocities will be exchanged
Option D
Speed = distance/time
since the question has instantaneous speed as constant, it means distance covered(path) in a time is constant / equal
rest of the options are related to velocity but not speed
Boyle's law holds true for a system if there is no addition of energy i.e PV=constant
In this case we are doing some work to pump air into the tyre so the energy is added into the system and thus the temperature will also increase inside the tyre and boyle's law is applied for constant temperature only
So membrane tension is 5 N/m which is given to find the pressure inside the sphere. The figure shows the forces along the membrane and pressure inside sphere
So the force by membrane = 2*pi*R*sigma = 2*pi*8*5 = 80*pi N
Force by the pressure inside = Area*Pressure = pi*R*R*P
Now use the formula PM = dRT
Now use the Pabs found and substitute to find density d (T is in kelvins)
M for air = 28.97 g/mol
Similarly, find the density of air outside balloon and find the buoyancy force acting on balloon and subtract buoyancy with weight of ballon then you will the weight it can carry
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