Linux:¿Sudo no puede abrir /etc/sudoers?

sudo no funciona.
Tengo Arch Linux instalado en una llave USB formateada con BTRFS.
Aquí está el resultado cuando ejecuto 'sudo':

$ sudo
sudo: unable to stat /etc/sudoers: Permission denied
sudo: no valid sudoers sources found, quitting
sudo: unable to initialize policy plugin

$ ls -l /etc/sudoers
-r--r----- 1 root root 2849 May 18 15:00 /etc/sudoers

$ lsattr /etc/sudoers
--------------- /etc/sudoers

$ ls -ld /etc
drwxr-xr-x 1 root root 2476 May 25 13:45 /etc

$ ls -ld /
drwx------ 1 root root 142 May 25 06:51 /

$ ls -l $(which sudo)
---s--x--x 2 root root 123995 May 25 13:10 /usr/bin/sudo

$ strace -u ross sudo true 2>&1 | egrep '(sudo|set.*[ug].*id)'
execve("/usr/bin/sudo", ["sudo", "true"], [/* 30 vars */]) = 0
read(3, "31799 (sudo) R 31796 31796 31754"..., 1024) = 223
lstat64("/etc/sudo.conf", 0xbfcddeb0)   = -1 ENOENT (No such file or directory)
stat64("/usr/lib/sudoers.so", {st_mode=S_IFREG|0755, st_size=235092, ...}) = 0
open("/usr/lib/sudoers.so", O_RDONLY|O_CLOEXEC) = 3
stat64("/usr/lib/sudoers.so", {st_mode=S_IFREG|0755, st_size=235092, ...}) = 0
setresuid32(0, -1, -1)                  = 0
setresgid32(-1, 0, -1)                  = 0
setresuid32(-1, 1, -1)                  = 0
lstat64("/etc/sudoers", 0xbfcddd60)     = -1 EACCES (Permission denied)
setresuid32(-1, 0, -1)                  = 0
write(2, "sudo", 4sudo)                     = 4
write(2, "unable to stat /etc/sudoers", 27unable to stat /etc/sudoers) = 27
setresuid32(-1, 1, -1)                  = 0
setresgid32(-1, -1, -1)                 = 0
setresuid32(-1, 0, -1)                  = 0
setresuid32(-1, 0, -1)                  = 0
setresgid32(-1, 1000, -1)               = 0
write(2, "sudo", 4sudo)                     = 4
write(2, "no valid sudoers sources found, "..., 40no valid sudoers sources found, quitting) = 40
write(2, "sudo", 4sudo)                     = 4


$ ltrace -u ross sudo true 2>&1 | egrep '(sudo|stat|set.*[ug].*id)'
bindtextdomain("sudo", "/usr/share/locale")      = "/usr/share/locale"
textdomain("sudo")                               = "sudo"
fopen("/proc/31813/stat", "r")                   = 0x9e51d40
__xstat(3, "/dev/console", 0xbffd6074)           = 0
__xstat(3, "/dev/wscons", 0xbffd6074)            = -1
__xstat(3, "/dev/pts/4", 0xbffd6074)             = 0
__lxstat64(3, "/etc/sudo.conf", 0xbffd9040)      = -1
strlen("sudo")                                   = 4
memcpy(0x09e51e71, "sudo", 4)                    = 0x09e51e71
__xstat64(3, "/usr/lib/sudoers.so", 0xbffd810c)  = 0
dlopen("/usr/lib/sudoers.so", 257 <unfinished ...>
dlsym(0x09e51ef8, "sudoers_policy")              = 0xb75af520
__xstat64(3, "/usr/lib/sudoers.so", 0xbffd810c)  = 0
dlopen("/usr/lib/sudoers.so", 257)               = 0x09e51ef8
dlsym(0x09e51ef8, "sudoers_io")                  = 0xb75af560
fputs("sudo", 0xb7760920sudo)                        = 1
fputs("unable to stat /etc/sudoers", 0xb7760920unable to stat /etc/sudoers) = 1
fputs("sudo", 0xb7760920sudo)                        = 1
fputs("no valid sudoers sources found, "..., 0xb7760920no valid sudoers sources found, quitting) = 1
fputs("sudo", 0xb7760920sudo)                        = 1
+++ exited (status 1) +++

Respuesta aceptada:

Vale, parece que no tienes acceso a / (no se puede reproducir un cd),

¿Puedes probar chmod 755 /?