Mechanics PYQ — Page 18

The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is

A particle moves in a straight line with a constant acceleration. It changes its velocity from $10 \mathrm{~ms}^{-1}$ to $20 \mathrm{~ms}^{-1}$ while passing through a distance $135 \mathrm{~m}$ in t second. The value of $t$ is

If the error in the measurement of radius of a sphere is $2 \%$, then the error in the determination of volume of the sphere will be

A shell of mass $200 \mathrm{~g}$ is ejected from a gun of mass $4 \mathrm{~kg}$ by an explosion that generates $1.05 \mathrm{~kJ}$ of energy. The initial velocity of the shell is

A particle moves in a straight line with a constant acceleration. It changes its velocity from $10 \mathrm{~ms}^{-1}$ to $20 \mathrm{~ms}^{-1}$ while passing through a distance $135 \mathrm{~m}$ in $t$ second. The value of $t$ is

A shell of mass $200 \mathrm{gm}$ is ejected from a gun of mass $4 \mathrm{~kg}$ by an explosion that generates $1.05 \mathrm{~kJ}$ of energy. The initial velocity of the shell is

The distance travelled by a particle starting from rest and moving with an acceleration $\frac{4}{3} \mathrm{~ms}^{-2}$, in the third second is

A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is $20 \mathrm{~m}$. The speed of the car at the top of the hill is between

The distance travelled by a particle starting from rest and moving with an acceleration $\frac{4}{3} \mathrm{~ms}^{-2}$, in the third second is

The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is

A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is $20 \mathrm{~m}$. The speed of the car at the top of the hill is between

A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point 

Water falls from a height of $60 \mathrm{~m}$ at the rate of $15 \mathrm{~kg} / \mathrm{s}$ to operate a turbine. The losses due to frictional forces are $10 \%$ of energy. How much power is generated by the turbine? $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)$

Three forces acting on a body are shown in the figure. To have the resultant force only along the $y$-direction, the magnitude of the minimum additional force needed is 

Water falls from a height of $60 \mathrm{~m}$ at the rate of $15 \mathrm{~kg} / \mathrm{s}$ to operate a turbine. The losses due to frictional forces are $10 \%$ of energy. How much power is generated by the turbine? $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)$

A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point 

A particle of mass $m$ is projected with velocity $v$ making an angle of $45^{\circ}$ with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be

A thin rod of length $L$ and mass $M$ is bent at its midpoint into two halves so that the angle between them is $90^{\circ}$. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is

A particle of mass $m$ is projected with velocity $y$ making an angle of $45^{\circ}$ with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be

Sand is being dropped on a conveyor belt at the rate of $M \mathrm{~kg} / \mathrm{s}$. The force necessary to keep the belt moving with a constant velocity of $v \mathrm{~m} / \mathrm{s}$ will be

Sand is being dropped on a conveyor belt at the rate of $\mathrm{M} \mathrm{kg} / \mathrm{s}$. The force necessary to keep the belt moving with a constant velocity of $v \mathrm{~m} / \mathrm{s}$ will be

Which two of the following five physical parameters have the same dimensions? (a) energy density (b) refractive index (c) dielectric constant (d) Young's modulus (e) magnetic field

Two satellites of earth, $\mathrm{S}_1$ and $\mathrm{S}_2$ are moving in the same orbit. The mass of $S_1$ of four times the mass of $S_2$. Which one of the following statements is true?

The position $x$ of a particle with respect to time $t$ along $x$-axis is given by $x=9 t^2$ $-t^3$ where $x$ is in metres and $t$ in second. What will be the position of this particle when it achieves maximum speed along the $+x$ direction?