The upper half of an inclined plane with inclination $\phi$ is perfectly smooth, while the lower half is rough. $A$ body starting from rest at the top will again come to rest at the bottom, if the coefficient of friction for the lower half is given by-
The upper half of an inclined plane with inclination $\phi$ is perfectly smooth, while the lower half is rough. $A$ body starting from rest at the top will again come to rest at the bottom, if the coefficient of friction for the lower half is given by-
- A
$2 \sin \phi$
- B
$2 \cos \phi$
- C
$2 \tan \phi$
- D
$ \tan \phi$
Similar Questions
In an elastic collision of two billiard balls, which of the following quantities remain conserved during the short time of collision of the balls ? (i.e. when they are in contact)
$(a)$ Kinetic energy.
$(b)$ Total linear momentum.
Give reason for your answer in each case.
In an elastic collision of two billiard balls, which of the following quantities remain conserved during the short time of collision of the balls ? (i.e. when they are in contact)
$(a)$ Kinetic energy.
$(b)$ Total linear momentum.
Give reason for your answer in each case.
Two particles, $1$ and $2$ , each of mass $m$, are connected by a massless spring, and are on a horizontal frictionless plane, as shown in the figure. Initially, the two particles, with their center of mass at $x_0$, are oscillating with amplitude a and angular frequency $\omega$. Thus, their positions at time $t$ are given by $x_1(t)=\left(x_0+d\right)+a \sin \omega t$ and $x_2(t)=\left(x_0-d\right)-$ $a$ sin $\omega t$, respectively, where $d>2 a$. Particle $3$ of mass $m$ moves towards this system with speed $u_0=a \omega / 2$, and undergoes instantaneous elastic collision with particle 2 , at time $t_0$. Finally, particles $1$ and $2$ acquire a center of mass speed $v_{ cm }$ and oscillate with amplitude $b$ and the same angular frequency. . . . .
($1$) If the collision occurs at time $t_0=0$, the value of $v_{ cm } /(a \omega)$ will be
($2$) If the collision occurs at time $t_0=\pi /(2 \omega)$, then the value of $4 b^2 / a^2$ will be
Give the answer or quetion ($1$) and ($2$)
Two particles, $1$ and $2$ , each of mass $m$, are connected by a massless spring, and are on a horizontal frictionless plane, as shown in the figure. Initially, the two particles, with their center of mass at $x_0$, are oscillating with amplitude a and angular frequency $\omega$. Thus, their positions at time $t$ are given by $x_1(t)=\left(x_0+d\right)+a \sin \omega t$ and $x_2(t)=\left(x_0-d\right)-$ $a$ sin $\omega t$, respectively, where $d>2 a$. Particle $3$ of mass $m$ moves towards this system with speed $u_0=a \omega / 2$, and undergoes instantaneous elastic collision with particle 2 , at time $t_0$. Finally, particles $1$ and $2$ acquire a center of mass speed $v_{ cm }$ and oscillate with amplitude $b$ and the same angular frequency. . . . .
($1$) If the collision occurs at time $t_0=0$, the value of $v_{ cm } /(a \omega)$ will be
($2$) If the collision occurs at time $t_0=\pi /(2 \omega)$, then the value of $4 b^2 / a^2$ will be
Give the answer or quetion ($1$) and ($2$)
- [IIT 2024]
A ball is allowed to fall from a height of $10 \,m$. If there is $40 \%$ loss of energy due to impact, then after one impact ball will go up by ........ $m$
A ball is allowed to fall from a height of $10 \,m$. If there is $40 \%$ loss of energy due to impact, then after one impact ball will go up by ........ $m$
A particle of mass $m$ moving horizontally with $v_0$ strikes $a$ smooth wedge of mass $M$, as shown in figure. After collision, the ball starts moving up the inclined face of the wedge and rises to $a$ height $h$. Choose the correct statement related to the wedge $M$
A particle of mass $m$ moving horizontally with $v_0$ strikes $a$ smooth wedge of mass $M$, as shown in figure. After collision, the ball starts moving up the inclined face of the wedge and rises to $a$ height $h$. Choose the correct statement related to the wedge $M$
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$I$ - kinetic energy
$II$- gravitational potential energy
$III$ - momentum
Which of these quantities will change as this sphere moves around the circle?
$A$ small sphere is moving at $a$ constant speed in $a$ vertical circle. Below is a list of quantities that could be used to describe some aspect of the motion of the sphere.
$I$ - kinetic energy
$II$- gravitational potential energy
$III$ - momentum
Which of these quantities will change as this sphere moves around the circle?