302 - Mechanics part 1 Questions Answers
a large open tank has two holes in the wall. one is a square hole of side L at a depth Y from the top and the other is a circular hole of radius R At a depth 4Y from the top . when the tank is completely filled with H2O , the quantities of H2O flowing / sec from both holes are same . then R IS equal to??
ans L / [√(2π)]
speed of water from any hole = √2gh
so volume of water per sec. = A√2gh
for square hole volume/sec = L2√2gY
for circular hole volume/sec = πR2√2g4Y
compare and get answer
An open knife edge of mass m is dropped from a height h on a wooden floor. if the blade penetrates a dist s into the wood , the avg. resistance offered by wood to blade. ANS mg(1+h/s)
velocity at the time of strike of the knife at the wood = √(2gh)
now equation for penetration on the wood is R-mg = ma here R is reaction by the wood
so R = m(g+a)
here it is given that s is the distance penetrated by the knife on the wood so 02 = (√2gh) - 2as so a = 2gh/2s = gh/s
on taking this value of a
we get R = m(g+gh/s) = mg(1+h/s)
A at road of 200km & B at 100km road. A with vel 20m/s & B with 7.5m/s . Then wat will b d time when B overtake A.
1) 24s
2) 40s
3) 80s
4)nothing can be predicted
data are irrelevent
A LIFT IS MOVING UPWARD WITH ACC 2m/s2 .WHEN IT GAIN THE VELOCITY 4m/s THEN AT THAT MOMENT A BALL IS PROJECTED BY 300 (wrt floor to lift) WITH VEL. 4m/s RELATIVE TO LIFT . FIND HOW MUCH TIME WILL IT TAKE TO 1) TO REACH GROUND & 2) TO THE FLOOR OF LIFT AGAIN
since velocity of the ball is 4 m/s relative to lift so
time taken by the ball to reach the floor of lift T = 2usinθ/g = (2*4*1/2)/10 = 0.4 sec
height of the lift at the time of dropping the ball = (v2-u2)/2g = 16/20 = 8/10 = 0.8 m = h
and vertical component of the velocity of ball with respect to the ground = 6 m/s = u
so use -h = ut - gt2/2
QUES A MAN RUNS AT A SPEED OF 4M/s TO OVERTAKE A STANDING BUS . WHEN HE IS 6m BEHIND THE DOOR (AT t=0) , THE BUS MOVES FORWARD & CONTINUES WITH A CONSTANT ACCELERATn OF 1.2m/s2 . the MAN SHALL GAIN THE DOOR AT TIME t EQUAL TO
A) 5.2s
b) 4.3s
c)2.3s
d) the man shell never gain the door.
ans 4.3s , Sir ,on solving I 'm getting both 4.3 & 2.3 s ( when we solve sq root) so here i want to know why not the ans is 2.3s. AMU 2012
After 2.3 sec. the man overtake the door first, in this time velocity of bus will be less than that of man so it is not possible to catch the bus then after 4.3 sec. the bus door will again reach to the man, in this time velocity of bus and man are same, so relative velocity is zero and catching of bus is possible.
velocity of impact = √2gh
so components of velocity after rebound = √2ghcosθ perpendicular to the plane and √2ghsinθ parallel to the plane for the collision is perfectly elestic
now with perpendicular component take net displacement 0 and calculate time
then find displacement along the plane by using s = ut + 1/2at2
here remember that you should divide gravity in comnents too
in first firing
m200 = 49mv so velocity of gun = 200/49
now apply momentum conservation again by taking 200/49 as the velocity of gun
my previous questn from rotational topic is still uncleared . I want to know why w= 4π is used.
according to rotational mechanics angular velocity = 2πn here n is frequency and in the problem n = 120 rotation/min = 2 rotation/sec.
the time period of oscillatn of a simple pendulum is 2π (l/g)1/2. l is about 10cm & is known to 1mm accuracy. the time period of oscillatn is about 0.5s . time of 100 oscillatn with a wrist watch of 1s revolutn . what is the accuracy in determinatn of g?
ans 5%
T = 2π (l/g)1/2
so g α l/T2
so % error in g = % error in l + 2 % error in T
= 0.1*100/10 + 2* 1*100/50 = 1+4 = 5
here you shoult remember that if you count 100 osccilations then time will be counted for 100 osccilation.
from rest a body rotate 120rot/min for 20 sec then rotate for 5 sec with same rotation . find how many rotation it will make?
here while calculating ang. acc you use w= w0 + at , how w=4π , ( i want to know how to convert 120 rot/min)
120 rotation per minute = 120/60 = 2 rotation per second