List of practice Questions

The time period of oscillation of a simple pendulum is $T = 2\pi\sqrt{\frac{l}{g}}$. Measured value of $l$ is $10\, cm$ known to $1$ mm accuracy and time for $100$ oscillations of the pendulum is found to be $50 \,s$ using a wrist watch of Is resolution. What is the accuracy in the determination of $g$ ?

Which of the following is an important intermediate found in all the types of respiration ?

A particle starts moving from rest under uniform acceleration . In travels a distance 'x' in the first two second and a distance 'y' in the next two second. If y=nx, then n

A particular solution of the equation $\log\frac{dy}{dx}=3x+4y,y(0)=0$ is

A passenger in a moving train tosses a coin. If the coin falls behind him, the train must be moving with

A pathway common to both anaerobic and aerobic metabolism is

A particle reaches its highest point at an instant of covering 1/2 of range. The corresponding position on displacement-time graph is characterised by.

A particle starting from rest moves upto $20\, s$ with constant acceleration. If $S _1$ is the distance covered in first $10\, s$ and $S_2$ is the distance covered in last $10$ second, then

A particle performs uniform circular motion with an angular momentum $L$. If the frequency of particle motion is doubled and its KE is halved the angular momentum becomes

A particle of mass m is attached to three identical massless springs of spring constant k as shown in the figure. The time period of vertical oscillation of the particle is .

A particle moves with uniform velocity. Which of the following statements about the motion of the particle is true ?

A particle of charge $q$ and mass $m$ is projected with a velocity $v_{0}$ towards a circular region having uniform Magnetic field $B$ perpendicular and into the plane of paper, from point $P$ as shown in figure. $R$ is the radius and $O$ is the centre of the circular region. If the line $OP$ makes an angle $\theta$ with the direction of $v_{0}$ then the value of $v_{0}$ so that particle passes through $O$ is

A particle moves rectilinearly. Its displacement $x$ at time $t$ is given by $x^2 = at^2 + b$ where $a$ and $b$ are constants. Its acceleration at time $t$ is proportional to

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

A particle moves in xy plane according to the law x = 4sin6t and y = 4(1 - cos6t). The distance traversed by the particle in 4 s is (x and y are in metres)

A particle moves along the curve $6y = x^3 + 2$. The point $?P?$ on the curve at which the y-coordinate is changing 8 times as fast as the x-coordinate, are $(4, 11)$ and $\left(-4, -\frac{31}{3}\right).$

A particle is projected with velocity $u$ inclined at an angle $\alpha$ with $x-axis$. Change in velocity of the particle on return to ground is

A particle is projected from the origin in $xy$ plane. Acceleration of particle in $y$ direction is $\alpha$ . Its equation of path of projectile is $y = ax-bx^2$, then initial velocity of the particle is

A particle is projected vertically upwards from a point A on the ground. It takes time $t_1$ to reach a point B, but it still continues to move up. If it takes further time $t_2$ to reach the ground from point B. Then height of point B from the ground is

A particle is projected from ground at an angle 45$^\circ$ with initial velocity $20\sqrt{2}ms^{-1}$. The magnitude of average velocity in a time interval from t = 0 to t = 3s in $ms^{-1}$ is.

A particle is moving on a circular path of radius $r$ with uniform speed $v$. What is the displacement of the particle after it has described an angle of $60^?$?

A particle is dropped from rest a large height, Assume $g$ to be constant throughout the motion. The time taken by it to fall through successive distances of $1\, m$ each will be

A particle experiences constant acceleration for 20 seconds after starting from rest. If it travels a distance $s_1$ in the first 10 seconds and distance $s_2$ in the next 10 seconds, then

A particle falls towards earth from infinity. The velocity with which it reaches earth's surface is.

A particle has a displacement of $12\,m$ towards east and $5\,m$ towards north and finally $6\,m$ vertically upwards. The sum of these displacement is