A ball is released from the top of a tower of height $h$ metres. It takes $T$ seconds to reach the ground. What is the position of the ball in $\mathrm { T } / 3$ seconds? (1) $\mathrm { h } / 9$ metres from the ground (2) $7 \mathrm {~h} / 9$ metres from the ground (3) $8 \mathrm {~h} / 9$ metres from the ground (4) $17 \mathrm {~h} / 18$ metres from the ground.
An automobile travelling with speed of $60 \mathrm {~km} / \mathrm { h }$, can brake to stop within a distance of 20 cm . If the car is going twice as fast, i.e $120 \mathrm {~km} / \mathrm { h }$, the stopping distance will be (1) 20 m (2) 40 m (3) 60 m (4) 80 m
A ball is thrown from a point with a speed $v _ { 0 }$ at an angle of projection $\theta$. From the same point and at the same instant person starts running with a constant speed $v _ { 0 } / 2$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection? (1) yes, $60 ^ { \circ }$ (2) yes, $30 ^ { \circ }$ (3) no (4) yes, $45 ^ { \circ }$
A projectile can have the same range $R$ for two angles of projection. If $T _ { 1 }$ and $T _ { 2 }$ be the time of flights in the two cases, then the product of the two time of flights is directly proportional to (1) $1 / R ^ { 2 }$ (2) $1 / R$ (3) R (4) $R ^ { 2 }$
If $t _ { 1 }$ and $t _ { 2 }$ are the times of flight of two particles having the same initial velocity $u$ and range R on the horizontal, then $t _ { 1 } ^ { 2 } + t _ { 2 } ^ { 2 }$ is equal to (1) $\frac { u ^ { 2 } } { g }$ (2) $\frac { 4 u ^ { 2 } } { g ^ { 2 } }$ (3) $\frac { u ^ { 2 } } { 2 g }$ (4) 1
A machine gun fires a bullet of mass 40 g with a velocity $1200 \mathrm {~ms} ^ { - 1 }$. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most? (1) one (2) four (3) two (4) three
A block rests on a rough inclined plane making an angle of $30 ^ { \circ }$ with the horizontal. The coefficient of static friction between the block and the plane is 0.8 . If the frictional force on the block is 10 N , the mass of the block (in kg ) is (take $\mathrm { g } = 10 \mathrm {~m} / \mathrm { s } ^ { 2 }$ ) (1) 2.0 (2) 4.0 (3) 1.6 (4) 2.5
A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to (1) $x ^ { 3 }$ (2) $e ^ { x }$ (3) $x$ (4) $\log _ { e } x$
A uniform chain of length 2 m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg . What is the work done in pulling the entire chain on the table? (1) 7.2 J (2) 3.6 J (3) 120 J (4) 1200 J
A force $\vec { F } = ( 5 \hat { i } + 3 \hat { j } + 2 \hat { k } ) N$ is applied over a particle which displaces it from its origin to the point $\vec { r } = ( 2 \hat { i } - \hat { j } ) m$. The work done on the particle in joules is (1) - 7 (2) + 7 (3) + 10 (4) + 13
A body of mass $m$, accelerates uniformly from rest to $v _ { 1 }$ in time $t _ { 1 }$. The instantaneous power delivered to the body as a function of time $t$ is (1) $\frac { m v _ { 1 } t } { t _ { 1 } }$ (2) $\frac { m v _ { 1 } ^ { 2 } t } { t _ { 1 } ^ { 2 } }$ (3) $\frac { m v _ { 1 } t ^ { 2 } } { t _ { 1 } }$ (4) $\frac { m v _ { 1 } ^ { 2 } t } { t _ { 1 } }$
A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected? (1) moment of inertia (2) angular momentum (3) angular velocity (4) rotational kinetic energy.
One solid sphere $A$ and another hollow sphere $B$ are of same mass and same outer radii. Their moment of inertia about their diameters are respectively $\mathrm { I } _ { \mathrm { A } }$ and $\mathrm { I } _ { \mathrm { B } }$ such that (1) $I _ { A } = I _ { B }$ (2) $I _ { A } > I _ { B }$ (3) $I _ { A } < I _ { B }$ (4) $I _ { A } / I _ { B } = d _ { A } / d _ { B }$ Where $d _ { A }$ and $d _ { B }$ are their densities.
A satellite of mass $m$ revolves around the earth of radius $R$ at a height $x$ from its surface. If $g$ is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is (1) $g x$ (2) $\frac { g R } { R - x }$ (3) $\frac { g ^ { 2 } } { R + x }$ (4) $\left( \frac { g R ^ { 2 } } { R + x } \right) ^ { 1 / 2 }$
The time period of an earth satellite in circular orbit is independent of (1) the mass of the satellite (2) radius of its orbit (3) both the mass and radius of the orbit (4) neither the mass of the satellite nor the radius of its orbit.
If $g$ is the acceleration due to gravity on the earth's surface, the gain in the potential energy of object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is (1) 2 mgR (2) $\frac { 1 } { 2 } \mathrm { mgR }$ (3) $\frac { 1 } { 4 } \mathrm { mgR }$ (4) mgR
Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to (1) $R ^ { \left( \frac { n + 1 } { 2 } \right) }$ (2) $R ^ { \left( \frac { n - 1 } { 2 } \right) }$ (3) $R ^ { n }$ (4) $\mathrm { R } ^ { \left( \frac { \mathrm { n } - 2 } { 2 } \right) }$
The bob of a simple pendulum executes simple harmonic motion in water with a period $t$, while the period of oscillation of the bob is $t _ { 0 }$ in air. Neglecting frictional force of water and given that the density of the bob is $\left( \frac { 4 } { 3 } \right) \times 1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$. What relationship between $t$ and $t _ { 0 }$ is true? (1) $t = t _ { 0 }$ (2) $t = t _ { 0 } / 2$ (3) $t = 2 t _ { 0 }$ (4) $t = 4 t _ { 0 }$
A particle at the end of a spring executes simple harmonic motion with a period $t _ { 1 }$, while the corresponding period for another spring is $t _ { 2 }$. If the period of oscillation with the two springs in series is $T$, then (1) $T = t _ { 1 } + t _ { 2 }$ (2) $T^2 = t_1^2 + t_2^2$ (3) $\mathrm { T } ^ { - 1 } = \mathrm { t } _ { 1 } ^ { - 1 } + \mathrm { t } _ { 2 } ^ { - 1 }$ (4) $\mathrm { T } ^ { - 2 } = \mathrm { t } _ { 1 } ^ { -2 } + \mathrm { t } _ { 2 } ^ { -2 }$
The total energy of a particle executing simple harmonic motion is (1) $\propto x$ (2) $\propto x ^ { 2 }$ (3) independent of $x$ (4) $\propto x ^ { 1 / 2 }$